Proving Correctness of Imperative Programs by Linearizing Constrained Horn Clauses

We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form $\{\varphi\}$ prog $\{\psi\}$, where the assertions $\varphi$ and $\psi$ are predicates defined by a set Spec of possibly recursive Horn clauses with linear arithmetic (LA) constraints in their premise (also called constrained Horn clauses). The verification method consists in constructing a set PC of constrained Horn clauses whose satisfiability implies that $\{\varphi\}$ prog $\{\psi\}$ is valid. We highlight some limitations of state-of-the-art constrained Horn clause solving methods, here called LA-solving methods, which prove the satisfiability of the clauses by looking for linear arithmetic interpretations of the predicates. In particular, we prove that there exist some specifications that cannot be proved valid by any of those LA-solving methods. These specifications require the proof of satisfiability of a set PC of constrained Horn clauses that contain nonlinear clauses (that is, clauses with more than one atom in their premise). Then, we present a transformation, called linearization, that converts PC into a set of linear clauses (that is, clauses with at most one atom in their premise). We show that several specifications that could not be proved valid by LA-solving methods, can be proved valid after linearization. We also present a strategy for performing linearization in an automatic way and we report on some experimental results obtained by using a preliminary implementation of our method.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

Enhancing Predicate Pairing with Abstraction for Relational Verification

Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called predicate pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the predicate pairing transformation can be enhanced by using various abstract domains based on linear arithmetic (i.e., the domain of convex polyhedra and some of its subdomains) during the transformation. After presenting an algorithm for predicate pairing with abstraction, we report on the experiments we have performed on over a hundred relational verification problems by using various abstract domains. The experiments have been performed by using the VeriMAP transformation and verification system, together with the Parma Polyhedra Library (PPL) and the Z3 solver for CHCs.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Solving non-linear Horn clauses using a linear Horn clause solver

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm then proceeds by applying the linearisation transformation and solver for linear Horn clauses to a sequence of sets of clauses with successively increasing dimension bound. The approach is then further developed by using a solution of clauses of lower dimension to (partially) linearise clauses of higher dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise.Comment: In Proceedings HCVS2016, arXiv:1607.0403

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

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing