3,740 research outputs found
12th International Workshop on Termination (WST 2012) : WST 2012, February 19â23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19â23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Polygraphs for termination of left-linear term rewriting systems
We present a methodology for proving termination of left-linear term
rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of
rewriting systems on algebraic circuits. We translate the considered TRS into a
polygraph of minimal size whose termination is proven with a polygraphic
interpretation, then we get back the property on the TRS. We recall Yves
Lafont's general translation of TRSs into polygraphs and known links between
their termination properties. We give several conditions on the original TRS,
including being a first-order functional program, that ensure that we can
reduce the size of the polygraphic translation. We also prove sufficient
conditions on the polygraphic interpretations of a minimal translation to imply
termination of the original TRS. Examples are given to compare this method with
usual polynomial interpretations.Comment: 15 page
Complexity Bounds for Ordinal-Based Termination
`What more than its truth do we know if we have a proof of a theorem in a
given formal system?' We examine Kreisel's question in the particular context
of program termination proofs, with an eye to deriving complexity bounds on
program running times.
Our main tool for this are length function theorems, which provide complexity
bounds on the use of well quasi orders. We illustrate how to prove such
theorems in the simple yet until now untreated case of ordinals. We show how to
apply this new theorem to derive complexity bounds on programs when they are
proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability
Problems (RP 2014, 22-24 September 2014, Oxford
The 2D Dependency Pair Framework for Conditional Rewrite SystemsÂżPart II: Advanced Processors and Implementation Techniques
[EN] Proving termination of programs in `real-lifeÂż 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.; GutiĂ©rrez Gil, R. (2020). The 2D Dependency Pair Framework for Conditional Rewrite SystemsÂżPart 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(1â2), 133â178 (2000)AlarcĂłn, B., GutiĂ©rrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with MU-TERM. In: Proceedings of AMASTâ10, LNCS, vol. 6486, pp. 201â208 (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., DurĂĄn, F., Eker, S., Lincoln, P., MartĂ-Oliet, N., Meseguer, J., Talcott, C.: All About MaudeâA High-Performance Logical Framework. LNCS 4350, Springer, New York (2007)Contejean, E., MarchĂ©, C., TomĂĄs, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Autom. Reason. 34(4), 325â363 (2006)Dershowitz, N.: A note on simplification orderings. Inf. Process. Lett. 9(5), 212â215 (1979)DurĂĄn, F., Lucas, S., Meseguer, J.: MTT: the Maude termination tool (system description). In: Proceedings of IJCARâ08, LNAI, vol. 5195, pp. 313â319 (2008)Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(2â3), 195â220 (2008)Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic Termination proofs in the dependency pair framework. In: Proceeding of IJCARâ06, LNAI, vol. 4130, pp. 281â286 (2006)Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: combining techniques for automated termination proofs. In: Proceedings of LPARâ04, LNAI, vol. 3452, pp. 301â331 (2004)Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reason. 37(3), 155â203 (2006)Goguen, J., Meseguer, J.: Models and equality for logical programming. In: Proceedings of TAPSOFTâ87, LNCS, vol. 250, pp. 1â22 (1987)GutiĂ©rrez, R., Lucas, S.: Automatic generation of logical models with AGES. In: Proceedings of CADE 2019, LNCS, vol. 11716, pp. 287â299 (2019). Tool page: http://zenon.dsic.upv.es/ages/Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: Proceedings of RTAâ04, LNCS, vol. 3091, pp. 249â268 (2004)Hodges, W.: Elementary predicate logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 1, pp. 1â131. 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., GutiĂ©rrez, R.: Automatic synthesis of logical models for order-sorted first-order theories. J. Autom. Reason. 60(4), 465â501 (2018)Lucas, S., GutiĂ©rrez, R.: Use of logical models for proving infeasibility in term rewriting. Inf. Process. Lett. 136, 90â95 (2018)Lucas, S., MarchĂ©, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inf. Process. Lett. 95, 446â453 (2005)Lucas, S., Meseguer, J.: Models for logics and conditional constraints in automated proofs of termination. In: Proceedings of AISCâ14, LNAI, vol. 8884, pp. 9â20 (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, WRLAâ14, LNCS, vol. 8663, pp. 195â212 (2014)Lucas, S., Meseguer, J.: Dependency pairs for proving termination properties of conditional term rewriting systems. J. Log. Algebr. Methods Program. 86, 236â268 (2017)Lucas, S., Meseguer, J.: Normal forms and normal theories in conditional rewriting. J. Log. Algebr. Methods Program. 85(1), 67â97 (2016)Lucas, S., Meseguer, J., GutiĂ©rrez, R.: Extending the 2D DP framework for conditional term rewriting systems. In: Selected Papers from LOPSTRâ14, LNCS, vol. 8981, pp. 113â130 (2015)Lucas, S., Meseguer, J., GutiĂ©rrez, R.: The 2D dependency pair framework for conditional rewrite systems. Part I: Definition and basic processors. J. Comput. Syst. Sci. 96, 74â106 (2018)McCune, W.: Prover9 & Mace4. http://www.cs.unm.edu/~mccune/prover9/ (2005â2010)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, 659â688 (2010)Sternagel, T., Middeldorp, A.: Conditional confluence (system description). In: Proceedings of RTA-TLCAâ14, LNCS, vol. f8560, pp. 456â465 (2014)Sternagel, T., Middeldorp, A.: Infeasible conditional critical pairs. In: Proceedings of IWCâ15, pp. 13â18 (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 IJCARâ04, LNAI, vol. 3097, pp. 75â90 (2004)Wang, H.: Logic of many-sorted theories. J. Symb. Log. 17(2), 105â116 (1952
Solving polynomial constraints for proving termination of rewriting
A termination problem can be transformed into a set of polynomial constraints. Up to now, several approaches have been studied to deal with these constraints as constraint solving problems. In this thesis, we study in depth some of these approaches, present some advances in each approach.Navarro Marset, RA. (2008). Solving polynomial constraints for proving termination of rewriting. http://hdl.handle.net/10251/13626Archivo delegad
Encoding TLA+ set theory into many-sorted first-order logic
We present an encoding of Zermelo-Fraenkel set theory into many-sorted
first-order logic, the input language of state-of-the-art SMT solvers. This
translation is the main component of a back-end prover based on SMT solvers in
the TLA+ Proof System
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. GutiĂ©rrez also supported by Juan de la Cierva Fellowship JCI-2012-13528.Lucas Alba, S.; GutiĂ©rrez 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/s10817-017-9419-3S465501604AlarcĂłn, B., GutiĂ©rrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with MU-TERM. In: Proceedings of AMASTâ10. LNCS, vol. 6486, pp. 201â208 (2011)AlarcĂłn, B., Lucas, S., Navarro-Marset, R.: Using matrix interpretations over the reals in proofs of termination. In: Proceedings of PROLEâ09, pp. 255â264 (2009)Albert, E., Genaim, S., GutiĂ©rrez, R.: A Transformational Approach to Resource Analysis with Typed-Norms. Revised Selected Papers from LOPSTRâ13. LNCS, vol. 8901, pp 38â53 (2013)de Angelis, E., Fioravante, F., Pettorossi, A., Proietti, M.: Proving correctness of imperative programs by linearizing constrained Horn clauses. Theory Pract. Log. 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