Context-Sensitive Dependency Pairs Framework

We show how to develop a dependency pair framework for proving termination of context-sensitive rewriting.Gutiérrez Gil, R. (2008). Context-Sensitive Dependency Pairs Framework. http://hdl.handle.net/10251/13625Archivo delegad

Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories

[EN] In program analysis, the synthesis of models of logical theories representing the program semantics is often useful to prove program properties. We use order-sorted first- order logic as an appropriate framework to describe the semantics and properties of programs as given theories. Then we investigate the automatic synthesis of models for such theories. We use convex polytopic domains as a flexible approach to associate different domains to different sorts. We introduce a framework for the piecewise definition of functions and predicates. We develop its use with linear expressions (in a wide sense, including linear transformations represented as matrices) and inequalities to specify functions and predicates. In this way, algorithms and tools from linear algebra and arithmetic constraint solving (e.g., SMT) can be used as a backend for an efficient implementation.Partially supported by the EU (FEDER), projects TIN2015-69175-C4-1-R, and GV PROMETEOII/2015/ 013. R. Gutiérrez also supported by Juan de la Cierva Fellowship JCI-2012-13528.Lucas Alba, S.; Gutiérrez Gil, R. (2018). Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories. Journal of Automated Reasoning. 60(4):465-501. https://doi.org/10.1007/s10817-017-9419-3S465501604Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with MU-TERM. In: Proceedings of AMAST’10. LNCS, vol. 6486, pp. 201–208 (2011)Alarcón, B., Lucas, S., Navarro-Marset, R.: Using matrix interpretations over the reals in proofs of termination. In: Proceedings of PROLE’09, pp. 255–264 (2009)Albert, E., Genaim, S., Gutiérrez, R.: A Transformational Approach to Resource Analysis with Typed-Norms. Revised Selected Papers from LOPSTR’13. LNCS, vol. 8901, pp 38–53 (2013)de Angelis, E., Fioravante, F., Pettorossi, A., Proietti, M.: Proving correctness of imperative programs by linearizing constrained Horn clauses. Theory Pract. Log. Program. 15(4–5), 635–650 (2015)de Angelis, E., Fioravante, F., Pettorossi, A., Proietti, M.: Semantics-based generation of verification conditions by program specialization. In: Proceedings of PPDP’15, pp. 91–102. ACM Press, New York (2015)Aoto, T.: Solution to the problem of zantema on a persistent property of term rewriting systems. J. Funct. Log. Program. 2001(11), 1–20 (2001)Barwise, J.: An Introduction to First-Order Logic. In: Barwise, J. (ed.) Handbook of Mathematical Logic. North-Holland, Amsterdam (1977)Barwise, J.: Axioms for Abstract Model Theory. Ann. Math. Log. 7, 221–265 (1974)Bochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry. Springer, Berlin (1998)Birkhoff, G., Lipson, J.D.: Heterogeneous algebras. J. Comb. Theory 8, 115–133 (1970)Bofill, M., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: The Barcelogic SMT Solver. In: Proceedings of CAV’08. LNCS, vol. 5123, pp. 294–298 (2008)Bjørner, N., Gurfinkel, A., McMillan, K., Rybalchenko, A.: Horn-clause solvers for program verification. In: Fields of Logic and Computation II—Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday. LNCS, vol. 9300, pp. 24–51 (2015)Bjørner, N., McMillan, K., Rybalchenko, A.: On solving universally quantified horn-clauses. In: Proceedings of SAS’13. LNCS vol. 7935, pp. 105–125 (2013)Bjørner, N., McMillan, K., Rybalchenko, A.: Program verification as satisfiability modulo theories. In: Proceedings of SMT’12, EPiC Series in Computing, vol. 20, pp. 3–11 (2013)Bliss, G.A.: Algebraic Functions. Dover (2004)Bonfante, G., Marion, J.-Y., Moyen, J.-Y.: On Lexicographic Termination Ordering With Space Bound Certifications. Revised Papers from PSI 2001. LNCS, vol. 2244, pp. 482–493 (2001)Boolos, G.S., Burgess, J.P., Jeffrey, R.C.: Computability and Logic, 4th edn. Cambridge University Press, Cambridge (2002)Borralleras, C., Lucas, S., Oliveras, A., Rodríguez, E., Rubio, A.: SAT modulo linear arithmetic for solving polynomial constraints. J. Autom. Reason. 48, 107–131 (2012)Bürckert, H.-J., Hollunder, B., Laux, A.: On Skolemization in constrained logics. Ann. Math. Artif. Intell. 18, 95–131 (1996)Burstall, R.M., Goguen, J.A.: Putting Theories together to make specifications. In: Proceedings of IJCAI’77, pp. 1045–1058. William Kaufmann (1977)Caplain, M.: Finding invariant assertions for proving programs. In: Proceedings of the International Conference on Reliable Software, pp. 165–171. ACM Press, New York (1975)Chang, C.L., Lee, R.C.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, Orlando (1973)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude—A High-Performance Logical Framework. LNCS 4350, (2007)Cohn, A.G.: Improving the expressiveness of many sorted logic. In: Proceedings of the National Conference on Artificial Intelligence, pp. 84–87. AAAI Press, Menlo Park (1983)Contejean, E., Marché, C., Tomás, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Autom. Reason. 34(4), 325–363 (2006)Cooper, D.C.: Programs for mechanical program verification. Mach. Intell. 6, 43–59 (1971). Edinburgh University PressCooper, D.C.: Theorem proving in arithmetic without multiplication. Mach. Intell. 7, 91–99 (1972)Courtieu, P., Gbedo, G., Pons, O.: Improved matrix interpretations. In: Proceedings of SOFSEM’10. LNCS, vol. 5901, pp. 283–295 (2010)Cousot, P., Cousot, R., Mauborgne, L.: Logical abstract domains and interpretations. In: The Future of Sofware Engineering, pp. 48–71. Springer, New York (2011)Cousot, P., Halbwachs, N.: Automatic Discovery of linear restraints among variables of a program. In: Conference Record of POPL’78, pp. 84–96. ACM Press, New York (1978)Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)Elspas, B., Levitt, K.N., Waldinger, R.J., Waksman, A.: An assessment of techniques for proving program correctness. Comput. Surv. 4(2), 97–147 (1972)van Emdem, M.H., Kowalski, R.A.: The semantics of predicate logic as a programming language. J. ACM 23(4), 733–742 (1976)Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. In: Proceedings of IJCAR’06. LNCS, vol. 4130, pp. 574–588 (2006)Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(2–3), 195–220 (2008)Floyd, R.W.: Assigning meanings to programs. Math. Asp. Comput. Sci. 19, 19–32 (1967)Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: Maximal termination. In: Proceedings of RTA’08. LNCS, vol. 5117, pp. 110–125 (2008)Fuhs, C., Giesl, J., Parting, M., Schneider-Kamp, P., Swiderski, S.: Proving termination by dependency pairs and inductive theorem proving. J. Autom. Reason. 47, 133–160 (2011)Fuhs, C., Kop, C.: Polynomial interpretations for higher-order rewriting. In: Proceedings of RTA’12. LIPIcs, vol. 15, pp. 176–192 (2012)Futatsugi, K., Diaconescu, R.: CafeOBJ Report. World Scientific, AMAST Series, (1998)Gaboardi, M., Péchoux, R.: On bounding space usage of streams using interpretation analysis. Sci. Comput. Program. 111, 395–425 (2015)Giesl, J., Mesnard, F., Rubio, A., Thiemann, R., Waldmann, J.: Termination competition (termCOMP 2015). In: Proceedings of CADE’15. LNCS, vol. 9195, pp. 105–108 (2015)Giesl, J., Ströder, T., Schneider-Kamp, P., Emmes, F., Fuhs, C.: Symbolic evaluation graphs and term rewriting—a general methodology for analyzing logic programs. In: Proceedings of the PPDP’12, pp. 1–12. ACM Press (2012)Giesl, J., Raffelsieper, M., Schneider-Kamp, P., Swiderski, S., Thiemann, R.: Automated termination proofs for haskell by term rewriting. ACM Trans. Program. Lang. Syst. 33(2), 7 (2011)Gnaedig, I.: Termination of Order-sorted Rewriting. In: Proceedings of ALP’92. LNCS, vol. 632, pp. 37–52 (1992)Goguen, J.A.: Order-Sorted Algebra. Semantics and Theory of Computation Report 14, UCLA (1978)Goguen, J.A., Burstall, R.M.: Some fundamental algebraic tools for the semantics of computation. Part 1: comma categories, colimits, signatures and theories. Theoret. Comput. Sci. 31, 175–209 (1984)Goguen, J.A., Burstall, R.M.: Some fundamental algebraic tools for the semantics of computation. Part 2 signed and abstract theories. Theoret. Comput. Sci. 31, 263–295 (1984)Goguen, J., Meseguer, J.: Models and equality for logical programming. In: Proceedings of TAPSOFT’87. LNCS, vol. 250, pp. 1–22 (1987)Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial algebra approach to the specification, correctness and implementation of abstract data types. In: Current Trends in Programming Methodology, pp. 80–149. Prentice Hall (1978)Goguen, J.A., Meseguer, J.: Remarks on remarks on many-sorted equational logic. Sigplan Notices 22(4), 41–48 (1987)Goguen, J., Meseguer, J.: Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoret. Comput. Sci. 105, 217–273 (1992)Goguen, J.A., Winkler, T., Meseguer, J., Futatsugi, K., Jouannaud, J.-P.: Introducing OBJ. In: Goguen, J., Malcolm, G. (eds.) Software Engineering with OBJ: Algebraic Specification in Action. Kluwer, Boston (2000)Grebenshikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: Proceedings of PLDI’12, pp. 405–416. ACM Press (2012)Gulwani, S., Tiwari, A.: Combining Abstract Interpreters. In: Proceedings of PLDI’06, pp. 376–386. ACM Press (2006)Gurfinkel, A., Kahsai, T., Komuravelli, A., Navas, J.A.: The seahorn verification framework. In: Proceedings of CAV’15, Part I. LNCS, vol. 9206, pp. 343–361 (2015)Gutiérrez, R., Lucas, S., Reinoso, P.: A tool for the automatic generation of logical models of order-sorted first-order theories. In: Proceedings of PROLE’16, pp. 215–230 (2016). http://zenon.dsic.upv.es/ages/Hantler, S.L., King, J.C.: An introduction to proving the correctness of programs. ACM Comput. Surv. 8(3), 331–353 (1976)Hayes, P.: A logic of actions. Mach. Intell. 6, 495–520 (1971). Edinburgh University Press, EdinburghHeidergott, B., Olsder, G.J., van der Woude, J.: Max plus at work. A course on max-plus algebra and its applications. In: Modeling and Analysis of Synchronized Systems, Princeton University Press (2006)Hirokawa, N., Moser, G.: Automated complexity analysis based on the dependency pair method. In: Proceedings of IJCAR 2008. LNCS, vol. 5195, pp. 364–379 (2008)Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576–583 (1969)Hodges, W.: Elementary Predicate Logic. Handbook of Philosophical Logic, vol. 1, pp. 1–131. Reidel Publishing Company (1983)Hodges, W.: A Shorter Model Theory. Cambridge University Press, Cambridge (1997)Hofbauer, D.: Termination proofs by context-dependent interpretation. In: Proceedings of RTA’01. LNCS, vol. 2051, pp. 108–121 (2001)Hofbauer, D.: Termination proofs for ground rewrite systems. interpretations and derivational complexity. Appl. Algebra Eng. Commun. Comput. 12, 21–38 (2001)Hofbauer, D., Lautemann, C.: Termination proofs and the length of derivations. In: Proceedings of RTA’89. LNCS, vol. 355, pp. 167–177 (1989)Hull, T.E., Enright, W.H., Sedgwick, A.E.: The correctness of numerical algorithms. In: Proceedings of PAAP’72, pp. 66–73 (1972)Igarashi, S., London, R.L., Luckham, D.: Automatic program verification I: a logical basis and its implementation. Acta Inform. 4, 145–182 (1975)Iwami, M.: Persistence of termination of term rewriting systems with ordered sorts. In: Proceedings of 5th JSSST Workshop on Programming and Programming Languages, Shizuoka, Japan, pp. 47–56. (2003)Iwami, M.: Persistence of termination for non-overlapping term rewriting systems. In: Proceedings of Algebraic Systems, Formal Languages and Conventional and Unconventional Computation Theory, Kokyuroku RIMS, University of Kyoto, vol. 1366, pp. 91–99 (2004)Katz, S., Manna, Z.: Logical analysis of programs. Commun. ACM 19(4), 188–206 (1976)Langford, C.H.: Review: Über deduktive Theorien mit mehreren Sorten von Grunddingen. J. Symb. Log. 4(2), 98 (1939)Lankford, D.S.: Some approaches to equality for computational logic: a survey and assessment. Memo ATP-36, Automatic Theorem Proving Project, University of Texas, Austin, TXLondon, R.L.: The current state of proving programs correct. In: Proceedings of ACM’72, vol. 1, pp. 39–46. ACM (1972)Lucas, S.: Polynomials over the reals in proofs of termination: from theory to practice. RAIRO Theor. Inform. Appl. 39(3), 547–586 (2005)Lucas, S.: Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving. Electron. Proc. Theor. Comput. Sci. 200, 32–47 (2015)Lucas, S.: Use of logical models for proving operational termination in general logics. In: Selected Papers from WRLA’16. LNCS, vol. 9942, pp. 1–21 (2016)Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inform. Proces. Lett. 95, 446–453 (2005)Lucas, S., Meseguer, J.: Models for logics and conditional constraints in automated proofs of termination. In: Proceedings of AISC’14. LNAI, vol. 8884, pp. 7–18 (2014)Lucas, S., Meseguer, J.: Order-sorted dependency pairs. In: Proceedings of PPDP’08 , pp. 108–119. ACM Press (2008)Lucas, S., Meseguer, J.: Proving operational termination of declarative programs in general logics. In: Proceedings of PPDP’14, pp. 111–122. ACM Digital Library (2014)Lucas, S., Meseguer, J.: Dependency pairs for proving termination properties of conditional term rewriting systems. J. Log. Algebr. Methods Program. 86, 236–268 (2017)Manna, Z.: The correctness of programs. J. Comput. Syst. Sci. 3, 119–127 (1969)Manna, Z.: Properties of programs and the first-order predicate calculus. J. ACM 16(2), 244–255 (1969)Manna, Z.: Termination of programs represented as interpreted graphs. In: Proceedings of AFIPS’70, pp. 83–89 (1970)Manna, Z., Ness, S.: On the termination of Markov algorithms. In: Proceedings of the Third Hawaii International Conference on System Science, pp. 789–792 (1970)Manna, Z., Pnueli, A.: Formalization of properties of functional programs. J. ACM 17(3), 555–569 (1970)Marion, Y.-I., Péchoux, R.: Sup-interpretations, a semantic method for static analysis of program resources. ACM Trans. Comput. Log. 10(4), 27 (2009)Martí-Oliet, N., Meseguer, J., Palomino, M.: Theoroidal maps as algebraic simulations. Revised Selected Papers from WADT’04. LNCS, vol. 3423, pp. 126–143 (2005)McCarthy, J.: Recursive functions of symbolic expressions and their computation by machine. Part I. Commun. ACM 3(4), 184–195 (1960)Meseguer, J.: General logics. In: Ebbinghaus, H.D., et al. (eds.) Logic Colloquium’87, pp. 275–329. North-Holland (1989)Meseguer, J., Skeirik, S.: Equational formulas and pattern operations in initial order-sorted algebras. Revised Selected Papers from LOPSTR’15. LNCS, vol. 9527, pp. 36–53 (2015)Middeldorp, A.: Matrix interpretations for polynomial derivational complexity of rewrite systems. In: Proceedings of LPAR’12. LNCS, vol. 7180, p. 12 (2012)Monin, J.-F.: Understanding Formal Methods. Springer, London (2003)Montenegro, M., Peña, R., Segura, C.: Space consumption analysis by abstract interpretation: inference of recursive functions. Sci. Comput. Program. 111, 426–457 (2015)de Moura, L., Bjørner, N.: Satisfiability modulo theories: introduction and applications. Commun. ACM 54(9), 69–77 (2011)Naur, P.: Proof of algorithms by general snapshots. Bit 6, 310–316 (1966)Neurauter, F., Middeldorp, A.: Revisiting matrix interpretations for proving termination of term rewriting. In: Proceedings of RTA’11. LIPICS, vol. 10, pp. 251–266 (2011)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, New York (2002)Ölveczky, P.C., Lysne, O.: Order-sorted termination: the unsorted way. In: Proceedings of ALP’96. LNCS, vol. 1139, pp. 92–106 (1996)Otto, C., Brockschmidt, M., von Essen, C., Giesl, J.: Automated termination analysis of java bytecode by term rewriting. In: Proceedings of RTA’10. LIPICS, vol. 6, pp. 259–276 (2010)Péchoux, R.: Synthesis of sup-interpretations: a survey. Theoret. Comput. Sci. 467, 30–52 (2013)Podelski, A., Rybalchenko, A.: Transition invariants. In: IEEE Computer Society Proceedings of LICS’04, pp. 32–41 (2004)Prestel, A., Delzell, C.N.: Positive Polynomials. From Hilbert’s 17th Problem to Real Algebra. Springer, Berlin (2001)Robinson, D.J.S.: A Course in Linear Algebra with Applications, 2nd edn. World Scientific Publishing, Co, Singapore (2006)Rümmer, P., Hojjat, H., Kuncak, V.: Disjunctive interpolants for horn-clause verification. In: Proceedings of CAV’13, vol. 8044, pp. 347–363 (2013)Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Amsterdam (1986)Schmidt, A.: Über deduktive Theorien mit mehreren Sorten von Grunddingen. Matematische Annalen 115(4), 485–506 (1938)Schmidt-Schauss, M.: Computational Aspects Of An Order-Sorted Logic With Term Declarations. PhD Thesis, Fachbereich Informatik der Universität Kaiserslautern (1988)Shapiro, S.: Foundations without Foundationalism: A Case for Second-Order Logic. Clarendon Press, New York (1991)Shostak, R.E.: A practical decision procedure for arithmetic with function symbols. J. ACM 26(2), 351–360 (1979)Smullyan, R.M.: Theory of Formal Systems. Princeton University Press, Princeton (1961)Tarski, A.: A Decision Method for Elementary Algebra and Geometry, 2nd edn. University of California Press, Berkeley (1951)Toyama, Y.: Counterexamples to termination for the direct sum of term rewriting systems. Inform. Process. Lett. 25, 141–143 (1987)Turing, A.M.: Checking a large routine. In: Report of a Conference on High Speed Automatic Calculating Machines, University Mathematics Laboratory, Cambridge, pp. 67–69 (1949)Urban, C.: The abstract domain of segmented ranking functions. In: Proceeding of SAS’13. LNCS, vol. 7935, pp. 43–62 (2013)Urban, C., Gurfinkel, A., Kahsai, T.: Synthesizing ranking functions from bits and pieces. In: Proceedings of TACAS’16. LNCS, vol. 9636, pp. 54–70 (2016)Waldmann, J.: Matrix interpretations on polyhedral domains. In: Proceedings of RTA’15. LIPICS, vol. 26, pp. 318–333 (2015)Waldmann, J., Bau, A., Noeth, E.: Matchbox termination prover. http://github.com/jwaldmann/matchbox/ (2014)Walther, C.: A mechanical solution of schubert’s steamroller by many-sorted resolution. Aritif. Intell. 26, 217–224 (1985)Wang, H.: Logic of many-sorted theories. J. Symb. Logic 17(2), 105–116 (1952)Zantema, H.: Termination of term rewriting: interpretation and type elimination. J. Symb. Comput. 17, 23–50 (1994

MU-TERM: Verify Termination Properties Automatically (System Description)

[EN] We report on the new version of mu-term, a tool for proving termination properties of variants of rewrite systems, including conditional, context-sensitive, equational, and order-sorted rewrite systems. We follow a unified logic-based approach to describe rewriting computations. The automatic generation of logical models for suitable first-order theories and formulas provide a common basis to implement the proofs.Supported by EU (FEDER), and projects RTI2018-094403-B-C32,PROMETEO/ 2019/098, and SP20180225. Also by INCIBE program "Ayudas para la excelencia de los equipos de investigación avanzada en ciberseguridad" (Raul Gutiérrez).Gutiérrez Gil, R.; Lucas Alba, S. (2020). MU-TERM: Verify Termination Properties Automatically (System Description). Springer Nature. 436-447. https://doi.org/10.1007/978-3-030-51054-1_28S436447Alarcón, B., et al.: Improving context-sensitive dependency pairs. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 636–651. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89439-1_44Alarcón, B., Gutiérrez, R., Lucas, S.: Context-sensitive dependency pairs. Inf. Comput. 208(8), 922–968 (2010). https://doi.org/10.1016/j.ic.2010.03.003Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with mu-term. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 201–208. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-17796-5_12Alarcón, B., Lucas, S., Meseguer, J.: A dependency pair framework for $${A} \vee {C}$$-termination. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 35–51. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16310-4_4Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236(1–2), 133–178 (2000). https://doi.org/10.1016/S0304-3975(99)00207-8Clavel, M., et al.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71999-1Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reasoning 40(2–3), 195–220 (2008). https://doi.org/10.1007/s10817-007-9087-9Giesl, J., Arts, T.: Verification of erlang processes by dependency pairs. Appl. Algebra Eng. Commun. Comput. 12(1/2), 39–72 (2001). https://doi.org/10.1007/s002000100063Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCoS 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005). https://doi.org/10.1007/11559306_12Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reasoning 37(3), 155–203 (2006). https://doi.org/10.1007/s10817-006-9057-7Goguen, J.A., Meseguer, J.: Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theor. Comput. Sci. 105(2), 217–273 (1992). https://doi.org/10.1016/0304-3975(92)90302-VGutiérrez, R., Lucas, S.: Function calls at frozen positions in termination of context-sensitive rewriting. In: Martí-Oliet, N., Ölveczky, P.C., Talcott, C. (eds.) Logic, Rewriting, and Concurrency. LNCS, vol. 9200, pp. 311–330. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23165-5_15Gutiérrez, R., Lucas, S.: Proving termination in the context-sensitive dependency pair framework. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 18–34. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16310-4_3Gutiérrez, R., Lucas, S.: Automatic generation of logical models with AGES. In: Fontaine, P. (ed.) CADE 2019. LNCS (LNAI), vol. 11716, pp. 287–299. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29436-6_17Gutiérrez, R., Lucas, S.: Automatically proving and disproving feasibility conditions. In: Peltier, N., Sofronie-Stokkermans, V. (eds.) IJCAR 2020. LNAI, vol. 12167, pp. 416–435. Springer, Heidelberg (2020)Lucas, S.: Context-sensitive computations in functional and functional logic programs. J. Funct. Log. Program. 1998(1), 1–61 (1998). http://danae.uni-muenster.de/lehre/kuchen/JFLP/articles/1998/A98-01/A98-01.htmlLucas, S.: Context-sensitive rewriting strategies. Inf. Comput. 178(1), 294–343 (2002). https://doi.org/10.1006/inco.2002.3176Lucas, S.: Proving semantic properties as first-order satisfiability. Artif. Intell. 277 (2019). https://doi.org/10.1016/j.artint.2019.103174Lucas, S., Gutiérrez, R.: Automatic synthesis of logical models for order-sorted first-order theories. J. Autom. Reasoning 60(4), 465–501 (2017). https://doi.org/10.1007/s10817-017-9419-3Lucas, S., Gutiérrez, R.: Use of logical models for proving infeasibility in term rewriting. Inf. Process. Lett. 136, 90–95 (2018). https://doi.org/10.1016/j.ipl.2018.04.002Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inf. Process. Lett. 95(4), 446–453 (2005). https://doi.org/10.1016/j.ipl.2005.05.002Lucas, S., Meseguer, J.: Order-sorted dependency pairs. In: Antoy, S., Albert, E. (eds.) Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, 15–17 July 2008, Valencia, Spain, pp. 108–119. ACM (2008). https://doi.org/10.1145/1389449.1389463Lucas, S., Meseguer, J.: Dependency pairs for proving termination properties of conditional term rewriting systems. J. Log. Algebraic Methods Program. 86(1), 236–268 (2017). https://doi.org/10.1016/j.jlamp.2016.03.003Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems. Part I: Definition and basic processors. J. Comput. Syst. Sci. 96, 74–106 (2018). https://doi.org/10.1016/j.jcss.2018.04.002Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems—part II: advanced processors and implementation techniques. J. Autom. Reasoning (2020). https://doi.org/10.1007/s10817-020-09542-3McCune, W.: Prover9 & Mace4. Technical report (2005–2010). http://www.cs.unm.edu/~mccune/prover9/Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer (2002). https://doi.org/10.1007/978-1-4757-3661-8 . http://www.springer.com/computer/swe/book/978-0-387-95250-5Ölveczky, P.C., Lysne, O.: Order-sorted termination: the unsorted way. In: Hanus, M., Rodríguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 92–106. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61735-3_6Zantema, H.: Termination of term rewriting: interpretation and type elimination. J. Symb. Comput. 17(1), 23–50 (1994). https://doi.org/10.1006/jsco.1994.1003Zantema, H.: Termination of context-sensitive rewriting. In: Comon, H. (ed.) RTA 1997. LNCS, vol. 1232, pp. 172–186. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-62950-5_6

infChecker. A Tool for Checking Infeasibility

[EN] Given a Conditional Term Rewriting System (CTRS) R and terms s and t, we say that the reachability condition s ->* t is *feasible* if there is a substitution \sigma instantiating the variables in s and t such that the *reachability test* \sigma(s)->* \sigma(t) succeeds; otherwise, we call it *infeasible*. Checking infeasibility of such (sequences of) reachability conditions is important in the analysis of computational properties of CTRSs, like confluence or operational termination. Recently, a logic-based approach to prove and disprove infeasibility has been introduced. In this paper we present infChecker, a new tool for checking infeasibility which is based on such an approach.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32, PROMETEO/2019/098, and SP20180225. Raul Gutierrez was also supported by INCIBE program Ayudas para la excelencia de los equipos de investigacion avanzada en ciberseguridad.Gutiérrez Gil, R.; Lucas Alba, S. (2019). infChecker. A Tool for Checking Infeasibility. Universidade de Brasilia. 38-42. http://hdl.handle.net/10251/181069S384

Order-Sorted Equality Enrichments Modulo Axioms

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for checking key properties such as confluence, termination, and sufficient completeness. Such specifications would instead be amenable to formal analysis if an equationally-defined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationally-defined equality predicate is very useful in its own right, particularly in inductive theorem proving. Is it possible to effectively define a theory transformation epsilon bar right arrow epsilon(similar to) that extends an algebraic specification epsilon to a specification epsilon(similar to) having an equationally-defined equality predicate? This paper answers this question in the affirmative for a broad class of order-sorted conditional specifications epsilon that are sort-decreasing, ground confluent, and operationally terminating modulo axioms B and have a subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativity-commutativity axioms, so that the constructors are free modulo B. We prove that the transformation epsilon bar right arrow epsilon(similar to) preserves all the just-mentioned properties of epsilon. The transformation has been automated in Maude using reflection and is used as a component in many Maude formal tools. (C) 2014 Elsevier B.V. All rights reserved.This work has been supported in part by NSF Grants CCF 09-05584 and CNS 13-19109, the EU (FEDER) and the Spanish MINECO under Grants TIN 2010-21062-C02 and TIN 2013-45732-C4-1-P, and by the Generalitat Valenciana, ref. PROMETEO/2011/052. Raul Gutierrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Gutiérrez Gil, R.; Meseguer, J.; Rocha, C. (2015). Order-Sorted Equality Enrichments Modulo Axioms. Science of Computer Programming. 99:235-261. https://doi.org/10.1016/j.scico.2014.07.003S2352619

The 2D Dependency Pair Framework for Conditional Rewrite Systems¿Part II: Advanced Processors and Implementation Techniques

[EN] Proving termination of programs in `real-life¿ rewriting-based languages like CafeOBJ, Haskell, Maude, etc., is an important subject of research. To advance this goal, faithfully cap- turing the impact in the termination behavior of the main language features (e.g., conditions in program rules) is essential. In Part I of this work, we have introduced a 2D Dependency Pair Framework for automatically proving termination properties of Conditional Term Rewriting Systems. Our framework relies on the notion of processor as the main practical device to deal with proofs of termination properties of conditional rewrite systems. Processors are used to decompose and simplify the proofs in a divide and conquer approach. With the basic proof framework defined in Part I, here we introduce new processors to further improve the abil- ity of the 2D Dependency Pair Framework to deal with proofs of termination properties of conditional rewrite systems. We also discuss relevant implementation techniques to use such processors in practice.Partially supported by the EU (FEDER) and projects RTI2018-094403-B-C32, PROMETEO/2019/098, SP20180225. Jose Meseguer was supported by grants NSF CNS 13-19109 and NRL N00173-17-1-G002. Salvador Lucas' research was partly developed during a sabbatical year at the UIUC.Lucas Alba, S.; Meseguer, J.; Gutiérrez Gil, R. (2020). The 2D Dependency Pair Framework for Conditional Rewrite Systems¿Part II: Advanced Processors and Implementation Techniques. Journal of Automated Reasoning. 64(8):1611-1662. https://doi.org/10.1007/s10817-020-09542-3S16111662648Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236(1–2), 133–178 (2000)Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with MU-TERM. In: Proceedings of AMAST’10, LNCS, vol. 6486, pp. 201–208 (2011)Baader, F., Nipkow, T.: Term Rewriting and all That. Cambridge University Press, Cambridge (1998)Barwise, J.: An introduction to first-order logic. In: Barwise, J. (ed.) Handbook of Mathematical Logic. North-Holland, Amsterdam (1977)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude—A High-Performance Logical Framework. LNCS 4350, Springer, New York (2007)Contejean, E., Marché, C., Tomás, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Autom. Reason. 34(4), 325–363 (2006)Dershowitz, N.: A note on simplification orderings. Inf. Process. Lett. 9(5), 212–215 (1979)Durán, F., Lucas, S., Meseguer, J.: MTT: the Maude termination tool (system description). In: Proceedings of IJCAR’08, LNAI, vol. 5195, pp. 313–319 (2008)Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(2–3), 195–220 (2008)Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic Termination proofs in the dependency pair framework. In: Proceeding of IJCAR’06, LNAI, vol. 4130, pp. 281–286 (2006)Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: combining techniques for automated termination proofs. In: Proceedings of LPAR’04, LNAI, vol. 3452, pp. 301–331 (2004)Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reason. 37(3), 155–203 (2006)Goguen, J., Meseguer, J.: Models and equality for logical programming. In: Proceedings of TAPSOFT’87, LNCS, vol. 250, pp. 1–22 (1987)Gutiérrez, R., Lucas, S.: Automatic generation of logical models with AGES. In: Proceedings of CADE 2019, LNCS, vol. 11716, pp. 287–299 (2019). Tool page: http://zenon.dsic.upv.es/ages/Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: Proceedings of RTA’04, LNCS, vol. 3091, pp. 249–268 (2004)Hodges, W.: Elementary predicate logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 1, pp. 1–131. Reidel Publishing Company, Dordrecht (1983)Lankford, D.S.: On proving term rewriting systems are noetherian. Technical Report, Louisiana Technological University, Ruston, LA (1979)Lucas, S.: Using Well-founded relations for proving operational termination. J. Autom. Reason. to appear (2020). https://doi.org/10.1007/s10817-019-09514-2Lucas, S., Gutiérrez, R.: Automatic synthesis of logical models for order-sorted first-order theories. J. Autom. Reason. 60(4), 465–501 (2018)Lucas, S., Gutiérrez, R.: Use of logical models for proving infeasibility in term rewriting. Inf. Process. Lett. 136, 90–95 (2018)Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inf. Process. Lett. 95, 446–453 (2005)Lucas, S., Meseguer, J.: Models for logics and conditional constraints in automated proofs of termination. In: Proceedings of AISC’14, LNAI, vol. 8884, pp. 9–20 (2014)Lucas, S., Meseguer, J.: 2D Dependency pairs for proving operational termination of CTRSs. In: Escobar, S., (ed) Proceedings of the 10th International Workshop on Rewriting Logic and its Applications, WRLA’14, LNCS, vol. 8663, pp. 195–212 (2014)Lucas, S., Meseguer, J.: Dependency pairs for proving termination properties of conditional term rewriting systems. J. Log. Algebr. Methods Program. 86, 236–268 (2017)Lucas, S., Meseguer, J.: Normal forms and normal theories in conditional rewriting. J. Log. Algebr. Methods Program. 85(1), 67–97 (2016)Lucas, S., Meseguer, J., Gutiérrez, R.: Extending the 2D DP framework for conditional term rewriting systems. In: Selected Papers from LOPSTR’14, LNCS, vol. 8981, pp. 113–130 (2015)Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems. Part I: Definition and basic processors. J. Comput. Syst. Sci. 96, 74–106 (2018)McCune, W.: Prover9 & Mace4. http://www.cs.unm.edu/~mccune/prover9/ (2005–2010)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, New York (2002)Schernhammer, F., Gramlich, B.: Characterizing and proving operational termination of deterministic conditional term rewriting systems. J. Log. Algebr. Program. 79, 659–688 (2010)Sternagel, T., Middeldorp, A.: Conditional confluence (system description). In: Proceedings of RTA-TLCA’14, LNCS, vol. f8560, pp. 456–465 (2014)Sternagel, T., Middeldorp, A.: Infeasible conditional critical pairs. In: Proceedings of IWC’15, pp. 13–18 (2014)Thiemann, R.: The DP Framework for Proving Termination of Term Rewriting. PhD Thesis, RWTH Aachen, Technical Report AIB-2007-17 (2007)Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Proceedings of IJCAR’04, LNAI, vol. 3097, pp. 75–90 (2004)Wang, H.: Logic of many-sorted theories. J. Symb. Log. 17(2), 105–116 (1952

A Dependency Pair Framework for AvC-Termination

The development of powerful techniques for proving termination of rewriting modulo a set of equational axioms is essential when dealing with rewriting logic-based programming languages like CafeOBJ, Maude, ELAN, OBJ, etc. One of the most important techniques for proving termination over a wide range of variants of rewriting (strategies) is the dependency pair approach. Several works have tried to adapt it to rewriting modulo associative and commutative (AC) equational theories, and even to more general theories. However, as we discuss in this paper, no appropriate notion of minimality (and minimal chain of dependency pairs) which is well-suited to develop a dependency pair framework has been proposed to date. In this paper we carefully analyze the structure of in nite rewrite sequences for rewrite theories whose equational part is any combination of associativity and/or commutativity axioms, which we call AvC-rewrite theories. Our analysis leads to a more accurate and optimized notion of dependency pairs through the new notion of stably minimal term. We then develop a suitable dependency pair framework for proving termination of AvC-rewrite theories.Alarcón Jiménez, B.; Gutiérrez Gil, R.; Lucas, S.; Meseguer, J. (2011). A Dependency Pair Framework for AvC-Termination. http://hdl.handle.net/10251/1079

Towards an Incremental and Modular Termination Analysis of Context-Sensitive Rewriting Systems (Work in Progress)

Modularity is essential in software development, where a piece of software is often designed and implemented as a composition of simpler modules. So, if we want to prove that a program satisfies a given property, a modular approach becomes natural. With the development and successful use of the Dependency Pair Framework, which rather focuses on the decomposition of termination problems, less attention has been payed to modularity issues (which rather require the opposite approach). But the modular analysis of termination is still paramount for software developers. In this paper, we analyze modularity of context-sensitive rewrite systems. A modularity analysis was carried out by Gramlich and Lucas in 2002, but a correct notion of context-sensitive dependency pair (CS-DP) was not obtained until 2006. In this paper, we analyze modularity using CS-DPs.Partially supported by the EU (FEDER), MINECO projects TIN2010-21062-C02-02 and TIN 2013-45732-C4-1-P, and project PROMETEO/2011/052. Salvador Lucas’ research was developed during a sabbatical year at the CS Dept. of the UIUC and was also partially supported by NSF grant CNS 13-19109, Spanish MECD grant PRX12/00214, and GV grant BEST/2014/026. Raúl Gutiérrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Gutiérrez Gil, R.; Lucas Alba, S. (2014). Towards an Incremental and Modular Termination Analysis of Context-Sensitive Rewriting Systems (Work in Progress). Sistedes. http://hdl.handle.net/10251/71781

Function Calls at Frozen Positions in Termination of Context-Sensitive Rewriting

Context-sensitive rewriting (CSR) is a variant of rewriting where only selected arguments of function symbols can be rewritten. Consequently, the subterm positions of a term are classified as either active, i.e., positions of subterms that can be rewritten; or frozen, i.e., positions that cannot. Frozen positions can be used to denote subexpressions whose evaluation is delayed or just forbidden. A typical example is the if-then-else operator whose second and third arguments are not evaluated until the evaluation of the first argument yields either true or false. Imposing replacement restrictions can improve the termination behavior of rewriting-based computational systems. Termination of CSR has been investigated by several authors and a number of automatic tools are able to prove it. In this paper, we analyze how frozen subterms affect termination of CSR. This analysis helps us to improve our context-sensitive dependency pair (CS-DP) framework for automatically proving termination of CSR. We have implemented these improvements in our tool MU-TERM. The experiments show the power of the improvements in practice.Gutiérrez Gil, R.; Lucas Alba, S. (2015). Function Calls at Frozen Positions in Termination of Context-Sensitive Rewriting. http://hdl.handle.net/10251/5075

A Bibliometric Diagnosis and Analysis about Smart Cities

[EN] This article aims to present a bibliometric analysis of Smart Cities. The study analyzes the most important journals during the period between 1991 and 2019. It provides helpful insights into the document types, the distribution of countries/territories, the distribution of institutions, the authors' geographical distribution, the most active authors and their research interests or fields, the relationships between principal authors and more relevant publications, and the most cited articles. This paper also provides important information about the core and historical references and the most cited papers. The analysis used the keywords and thematic noun-phrases in the titles and abstracts of the sample papers to explore the hot research topics in the top journals (e.g., 'Smart Cities', 'Intelligent Cities', 'Sustainable Cities', 'e-Government', 'Digital Transformation', 'Knowledge-Based City', etc.). The main objective is to have a quantitative description of the published literature about Smart Cities; this description will be the basis for the development of a methodology for the diagnosis of the maturity of a Smart City. The results presented here help to define the scientific concept of Smart Cities and to measure the importance that the term has gained through the years. The study has allowed us to know the main indicators of the published literature in depth, from the date of publication of the first articles and the evolution of these indicators to the present day. From the main indicators in the literature, some were selected to be applied: The most influential journals on Smart Cities according to the general citation structure in Smart Cities, Global Impact Factor of Smart Cities, number of publications, publications on Smart Cities around the world, and their correlation.Pérez, LM.; Oltra Badenes, RF.; Oltra Gutiérrez, JV.; Gil Gómez, H. (2020). A Bibliometric Diagnosis and Analysis about Smart Cities. Sustainability. 12(16):1-43. https://doi.org/10.3390/su12166357S1431216Guo, Y.-M., Huang, Z.-L., Guo, J., Li, H., Guo, X.-R., & Nkeli, M. J. (2019). Bibliometric Analysis on Smart Cities Research. Sustainability, 11(13), 3606. doi:10.3390/su11133606Mora, L., Bolici, R., & Deakin, M. (2017). The First Two Decades of Smart-City Research: A Bibliometric Analysis. Journal of Urban Technology, 24(1), 3-27. doi:10.1080/10630732.2017.1285123Albino, V., Berardi, U., & Dangelico, R. M. (2015). Smart Cities: Definitions, Dimensions, Performance, and Initiatives. Journal of Urban Technology, 22(1), 3-21. doi:10.1080/10630732.2014.942092Li, C., Liu, X., Dai, Z., & Zhao, Z. (2019). Smart City: A Shareable Framework and Its Applications in China. Sustainability, 11(16), 4346. doi:10.3390/su11164346Merigó, J. M., & Yang, J.-B. (2016). Accounting Research: A Bibliometric Analysis. Australian Accounting Review, 27(1), 71-100. doi:10.1111/auar.12109Garg, K. C., & Sharma, C. (2017). Bibliometrics of Library and Information Science research in India during 2004-2015. DESIDOC Journal of Library & Information Technology, 37(3), 221-227. doi:10.14429/djlit.37.3.11188Metse, A. P., Wiggers, J. H., Wye, P. M., Wolfenden, L., Prochaska, J. J., Stockings, E. A., … Bowman, J. A. (2016). Smoking and Mental Illness: A Bibliometric Analysis of Research Output Over Time. Nicotine & Tobacco Research, 19(1), 24-31. doi:10.1093/ntr/ntw249Broadus, R. N. (1987). Toward a definition of «bibliometrics». Scientometrics, 12(5-6), 373-379. doi:10.1007/bf02016680Hood, W. W., & Wilson, C. S. (2001). Scientometrics, 52(2), 291-314. doi:10.1023/a:1017919924342Thelwall, M. (2008). Bibliometrics to webometrics. Journal of Information Science, 34(4), 605-621. doi:10.1177/0165551507087238Bar-Ilan, J. (2008). Informetrics at the beginning of the 21st century—A review. Journal of Informetrics, 2(1), 1-52. doi:10.1016/j.joi.2007.11.001Narin, F., Olivastro, D., & Stevens, K. A. (1994). Bibliometrics/Theory, Practice and Problems. Evaluation Review, 18(1), 65-76. doi:10.1177/0193841x9401800107Zupic, I., & Čater, T. (2014). Bibliometric Methods in Management and Organization. Organizational Research Methods, 18(3), 429-472. doi:10.1177/1094428114562629OSAREH, F. (1996). Bibliometrics, Citation Analysis and Co-Citation Analysis: A Review of Literature I. Libri, 46(3). doi:10.1515/libr.1996.46.3.149Merigó, J. M., Gil-Lafuente, A. M., & Yager, R. R. (2015). An overview of fuzzy research with bibliometric indicators. Applied Soft Computing, 27, 420-433. doi:10.1016/j.asoc.2014.10.035Blanco-Mesa, F., Merigó, J. M., & Gil-Lafuente, A. M. (2017). Fuzzy decision making: A bibliometric-based review. Journal of Intelligent & Fuzzy Systems, 32(3), 2033-2050. doi:10.3233/jifs-161640Björneborn, L., & Ingwersen, P. (2004). Toward a basic framework for webometrics. Journal of the American Society for Information Science and Technology, 55(14), 1216-1227. doi:10.1002/asi.20077Gupta, B. . M., & Dhawan, S. (2019). Electronic books A scientometric assessment of global literature during 1993 2018. DESIDOC Journal of Library & Information Technology, 39(5), 251-258. doi:10.14429/djlit.39.5.14573Kokol, P., Blažun Vošner, H., & Završnik, J. (2020). Application of bibliometrics in medicine: a historical bibliometrics analysis. Health Information & Libraries Journal, 38(2), 125-138. doi:10.1111/hir.12295Michalopoulos, A., & Falagas, M. E. (2005). A Bibliometric Analysis of Global Research Production in Respiratory Medicine. Chest, 128(6), 3993-3998. doi:10.1378/chest.128.6.3993Lefaivre, K. A., Shadgan, B., & O’Brien, P. J. (2011). 100 Most Cited Articles in Orthopaedic Surgery. Clinical Orthopaedics & Related Research, 469(5), 1487-1497. doi:10.1007/s11999-010-1604-1Kelly, J. C., Glynn, R. W., O’Briain, D. E., Felle, P., & McCabe, J. P. (2010). The 100 classic papers of orthopaedic surgery. The Journal of Bone and Joint Surgery. British volume, 92-B(10), 1338-1343. doi:10.1302/0301-620x.92b10.24867Zhang, M., Zhou, Y., Lu, Y., He, S., & Liu, M. (2019). The 100 most-cited articles on prenatal diagnosis. Medicine, 98(38), e17236. doi:10.1097/md.0000000000017236Zou, Y., Luo, Y., Zhang, J., Xia, N., Tan, G., & Huang, C. (2019). Bibliometric analysis of oncolytic virus research, 2000 to 2018. Medicine, 98(35), e16817. doi:10.1097/md.0000000000016817Svider, P. F., Choudhry, Z. A., Choudhry, O. J., Baredes, S., Liu, J. K., & Eloy, J. A. (2012). The use of theh-indexin academic otolaryngology. The Laryngoscope, 123(1), 103-106. doi:10.1002/lary.23569Poskevicius, L., De la Flor-Martínez, M., Galindo-Moreno, P., & Juodzbalys, G. (2019). Scientific Publications in Dentistry in Lithuania, Latvia, and Estonia Between 1996 and 2018: A Bibliometric Analysis. Medical Science Monitor, 25, 4414-4422. doi:10.12659/msm.914223Ahmad, P., Asif, J. A., Alam, M. K., & Slots, J. (2019). A bibliometric analysis of Periodontology 2000. Periodontology 2000, 82(1), 286-297. doi:10.1111/prd.12328Kostoff, R. N., Toothman, D. R., Eberhart, H. J., & Humenik, J. A. (2001). Text mining using database tomography and bibliometrics: A review. Technological Forecasting and Social Change, 68(3), 223-253. doi:10.1016/s0040-1625(01)00133-0Grant, J. (2000). Evaluating «payback» on biomedical research from papers cited in clinical guidelines: applied bibliometric study. BMJ, 320(7242), 1107-1111. doi:10.1136/bmj.320.7242.1107Vergidis, P. I., Karavasiou, A. I., Paraschakis, K., Bliziotis, I. A., & Falagas, M. E. (2005). Bibliometric analysis of global trends for research productivity in microbiology. European Journal of Clinical Microbiology & Infectious Diseases, 24(5), 342-346. doi:10.1007/s10096-005-1306-xSuárez Roldan, C., Chaparro, N., & Rojas-Galeano, S. (2019). Análisis Bibliométrico de la Revista Ingeniería (2010-2017). Ingeniería, 24(2). doi:10.14483/23448393.14678Ratten, V., Pellegrini, M. M., Fakhar Manesh, M., & Dabić, M. (2020). Trends and changes in Thunderbird International Business Review journal: A bibliometric review. Thunderbird International Business Review, 62(6), 721-732. doi:10.1002/tie.22124Baker, H. K., Kumar, S., & Pattnaik, D. (2020). Fifty years of The Financial Review  : A bibliometric overview. Financial Review, 55(1), 7-24. doi:10.1111/fire.12228Charlesworth, M., Klein, A. A., & White, S. M. (2019). A bibliometric analysis of the conversion and reporting of pilot studies published in six anaesthesia journals. Anaesthesia, 75(2), 247-253. doi:10.1111/anae.14817Van Noorden, R., Maher, B., & Nuzzo, R. (2014). The top 100 papers. Nature, 514(7524), 550-553. doi:10.1038/514550aNicoll, L. H., Oermann, M. H., Carter‐Templeton, H., Owens, J. K., & Edie, A. H. (2020). A bibliometric analysis of articles identified by editors as representing excellence in nursing publication: Replication and extension. Journal of Advanced Nursing, 76(5), 1247-1254. doi:10.1111/jan.14316Liu, W., Wang, Z., & Zhao, H. (2020). Comparative study of customer relationship management research from East Asia, North America and Europe: A bibliometric overview. Electronic Markets, 30(4), 735-757. doi:10.1007/s12525-020-00395-7Cronin, B. (2001). Bibliometrics and beyond: some thoughts on web-based citation analysis. Journal of Information Science, 27(1), 1-7. doi:10.1177/016555150102700101Durieux, V., & Gevenois, P. A. (2010). Bibliometric Indicators: Quality Measurements of Scientific Publication. Radiology, 255(2), 342-351. doi:10.1148/radiol.09090626Guerola Navarro, V., Oltra Badenes, R. F., Gil Gomez, H., & Gil Gomez, J. A. (2020). Customer Relationship Management (CRM): A Bibliometric Analysis. International Journal of Services Operations and Informatics, 10(3), 1. doi:10.1504/ijsoi.2020.10030517Vicedo, P., Gil-Gómez, H., Oltra-Badenes, R., & Guerola-Navarro, V. (2020). A bibliometric overview of how critical success factors influence on enterprise resource planning implementations. Journal of Intelligent & Fuzzy Systems, 38(5), 5475-5487. doi:10.3233/jifs-179639Daim, T. U., Rueda, G., Martin, H., & Gerdsri, P. (2006). Forecasting emerging technologies: Use of bibliometrics and patent analysis. Technological Forecasting and Social Change, 73(8), 981-1012. doi:10.1016/j.techfore.2006.04.004Fersht, A. (2009). The most influential journals: Impact Factor and Eigenfactor. Proceedings of the National Academy of Sciences, 106(17), 6883-6884. doi:10.1073/pnas.0903307106Fu, H.-Z., Wang, M.-H., & Ho, Y.-S. (2013). Mapping of drinking water research: A bibliometric analysis of research output during 1992–2011. Science of The Total Environment, 443, 757-765. doi:10.1016/j.scitotenv.2012.11.061Fu, H., Ho, Y., Sui, Y., & Li, Z. (2010). A bibliometric analysis of solid waste research during the period 1993–2008. Waste Management, 30(12), 2410-2417. doi:10.1016/j.wasman.2010.06.008Wang, H., He, Q., Liu, X., Zhuang, Y., & Hong, S. (2012). Global urbanization research from 1991 to 2009: A systematic research review. Landscape and Urban Planning, 104(3-4), 299-309. doi:10.1016/j.landurbplan.2011.11.006Ellegaard, O., & Wallin, J. A. (2015). The bibliometric analysis of scholarly production: How great is the impact? Scientometrics, 105(3), 1809-1831. doi:10.1007/s11192-015-1645-