1,592 research outputs found

    Using Well-Founded Relations for Proving Operational Termination

    Full text link
    [EN] In this paper, we study operational termination, a proof theoretical notion for capturing the termination behavior of computational systems. We prove that operational termination can be characterized at different levels by means of well- founded relations on specific formulas which can be obtained from the considered system. We show how to obtain such well-founded relations from logical models which can be automatically generated using existing tools.Partially supported by the EU (FEDER), Projects TIN2015-69175-C4-1-R, and GV PROMETEOII/2015/013.Lucas Alba, S. (2020). Using Well-Founded Relations for Proving Operational Termination. Journal of Automated Reasoning. 64(2):167-195. https://doi.org/10.1007/s10817-019-09514-2S167195642Alarcón, 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, Springer (2011)Aguirre, L., Martí-Oliet, N., Palomino, M., Pita, I.: Sentence-normalized conditional narrowing modulo in rewriting logic and Maude. J. Automat. Reason. 60(4), 421–463 (2018)Arts, T., Giesl, J.: Proving innermost normalisation automatically. In: Proceedings of RTA’97, LNCS, vol. 1232, pp. 157–171, Springer, Berlin (1997)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236(1–2), 133–178 (2000)Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude—A High-Performance Logical Framework. LNCS, vol. 4350, Springer (2007)Durán, F., Lucas, S., Meseguer, J.: Methods for proving termination of rewriting-based programming languages by transformation. Electron. Notes Theor. Comput. Sci. 248, 93–113 (2009)Durán, F., Lucas, S., Marché, C., Meseguer, J., Urbain, X.: Proving operational termination of membership equational programs. High. Order Symb. Comput. 21(1–2), 59–88 (2008)Falke, S., Kapur, D.: Operational termination of conditional rewriting with built-in numbers and semantic data structures. Electron. Notes Theor. Comput. Sci. 237, 75–90 (2009)Floyd, R.W.: Assigning meanings to programs. Math. Asp. Comput. Sci. 19, 19–32 (1967)Giesl, J., Arts, T.: Verification of Erlang processes by dependency pairs. Appl. Algebra Eng. Commun. Comput. 12, 39–72 (2001)Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reason. 37(3), 155–203 (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., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: automatic termination proofs in the dependency pair framework. In: Proceedings of IJCAR’06, LNAI, vol. 4130, pp. 281–286 (2006)Goguen, J., Meseguer, J.: Models and equality for logical programming. In: Proceedings of TAPSOFT’87, LNCS, vol. 250, pp. 1–22 (1987)Goguen, J., Meseguer, J.: Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theor. Comput. Sci. 105, 217–273 (1992)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)Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean termination tool 2. In: Proceedings of RTA 2009, LNCS, vol. 5595, pp. 295–304 (2009)Lalement, R.: Computation as Logic. Masson-Prentice Hall International, Paris (1993)Lucas, S.: Context-sensitive rewriting strategies. Inf. Comput. 178(1), 294–343 (2002)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.: Directions of operational termination. In: Proceedings of PROLE’18. http://hdl.handle.net/11705/PROLE/2018/009 (2018). Accessed 9 Feb 2019Lucas, 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.: Dependency pairs for proving termination properties of conditional term rewriting systems. J. Log. Algebr. Methods Program. 86, 236–268 (2017)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)McCune, W.: Prover9 & Mace4. http://www.cs.unm.edu/~mccune/prover9/ (2005–2010). Accessed 9 Feb 2019Mendelson, E.: Introduction to Mathematical Logic, 4th edn. Chapman & Hall, London (1997)Meseguer, J.: General logics. In: Logic Colloquium’87, pp. 275–329 (1989)O’Donnell, M.J.: Equational Logic as a Programming Language. The MIT Press, Cambridge (1985)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Berlin (2002)Prawitz, D.: Natural Deduction. A Proof Theoretical Study. Almqvist & Wiksell, 1965. Reprinted by Dover Publications (2006)Rosu, G., Stefanescu, A., Ciobaca, S., Moore, B.M.: One-path reachability logic. In: Proceedings of LICS 2013, pp. 358–367. IEEE Press (2013)Shapiro, S.: Foundations Without Foundationalism: A Case for Second-Order Logic. Clarendon Press, Oxford (1991)Schernhammer, F., Gramlich, B.: Characterizing and proving operational termination of deterministic conditional term rewriting systems. J. Log. Algebr. Program. 79, 659–688 (2010)Serbanuta, T., Rosu, G.: Computationally equivalent elimination of conditions. In: Proceedings of RTA’06, LNCS, vol. 4098, pp. 19–34. Springer, Berlin (2006)Turing, A.M.: Checking a large routine. In: Report of a Conference on High Speed Automatic Calculating Machines, Univ. Math. Lab., Cambridge, pp. 67–69 (1949

    Automated Termination Analysis for Logic Programs with Cut

    Full text link
    Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator. We introduce a novel pre-processing method which automatically transforms Prolog programs into logic programs without cuts, where termination of the cut-free program implies termination of the original program. Hence after this pre-processing, any technique for proving termination of definite logic programs can be applied. We implemented this pre-processing in our termination prover AProVE and evaluated it successfully with extensive experiments

    Polynomial Path Orders: A Maximal Model

    Full text link
    This paper is concerned with the automated complexity analysis of term rewrite systems (TRSs for short) and the ramification of these in implicit computational complexity theory (ICC for short). We introduce a novel path order with multiset status, the polynomial path order POP*. Essentially relying on the principle of predicative recursion as proposed by Bellantoni and Cook, its distinct feature is the tight control of resources on compatible TRSs: The (innermost) runtime complexity of compatible TRSs is polynomially bounded. We have implemented the technique, as underpinned by our experimental evidence our approach to the automated runtime complexity analysis is not only feasible, but compared to existing methods incredibly fast. As an application in the context of ICC we provide an order-theoretic characterisation of the polytime computable functions. To be precise, the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*

    Non-termination using Regular Languages

    Get PDF
    We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.Comment: Published at International Workshop on Termination 201

    Proving Looping and Non-Looping Non-Termination by Finite Automata

    Get PDF
    A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic
    • …
    corecore