Abstract
The Knuth-Bendix method takes in argument a finite set of equations and rewrite rules and, when it succeeds, returns an algorithm to decide if a term is equivalent to another modulo these equations and rules. In this paper, we design a similar method that takes in argument a finite set of rewrite rules and, when it succeeds, returns an algorithm to decide not equivalence but reachability modulo these rules, that is if a term reduces to another. As an application, we give new proofs of the decidability of reachability in finite ground rewrite systems and in pushdown systems.
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References
Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)
Burel, G., Dowek, G., Jiang, Y.: Automata, resolution and cut-elimination (manuscript) (2015)
Dauchet, M., Tison, S.: Decidability of confluence for ground term rewriting systems. In: Budach, L. (ed.) FCT 1985. LNCS, vol. 199, pp. 80–89. Springer, Heidelberg (1985)
Dershowitz, N.: Completion and its applications. In: Aït-Kaci, H., Nivat, M. (eds.) Resolution of Equations in Algebraic Structures, vol. 2, chapter 2, pp. 31–86. Academic Press (1989)
Dershowitz, N., Manna, Z.: Proving termination with multiset orderings. Communications of the ACM 22(8), 465–476 (1979)
Dowek, G.: What is a theory? In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 50–64. Springer, Heidelberg (2002)
Dowek, G.: Confluence as a cut elimination property. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 2–13. Springer, Heidelberg (2003)
Dowek, G.: Polarized resolution modulo. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 182–196. Springer, Heidelberg (2010)
Hirokawa, N.: Commutation and signature extension. In: Tiwari, A., Aoto, T. (eds.) International Workshop on Confluence (2015)
Huet, G.: Confluent reductions: abstract properties and applications to term rewriting systems. Journal of the Association of Computing Machinery 27(4), 797–821 (1980)
Jouannaud, J.-P., Kirchner, H.: Completion of a set of rules modulo a set of equations. SIAM Journal of Computing 15(4), 1155–1194 (1986)
Kamin, S., Lévy, J.-J.: Attempts for generalizing the recursive path ordering (unpublished manuscript)
Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Computational Problems in Abstract Algebra, pp. 263–297, Pergamon (1970)
Lankford, D.S.: Canonical inference. Technical report, Louisiana Tech. University (1975)
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Burel, G., Dowek, G., Jiang, Y. (2015). A Completion Method to Decide Reachability in Rewrite Systems. In: Lutz, C., Ranise, S. (eds) Frontiers of Combining Systems. FroCoS 2015. Lecture Notes in Computer Science(), vol 9322. Springer, Cham. https://doi.org/10.1007/978-3-319-24246-0_13
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DOI: https://doi.org/10.1007/978-3-319-24246-0_13
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