Abstract
Decision procedures for various list theories have been investigated in the literature with applications to automated verification. Here we show that the unifiability problem for some list theories with a reverse operator is NP-complete. We also give a unifiability algorithm for the case where the theories are extended with a length operator on lists.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Anantharaman, S., Hibbs, P., Narendran, P., Rusinowitch, M.: Unification of lists with reverse as solving simple sets of word equations. Research-Report. https://hal.archives-ouvertes.fr/hal-02123648
Abdulla, P.A., et al.: String constraints for verification. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 150–166. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_10
Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. ACM Trans. Comput. Log. 10(1), 4:1–4:51 (2009)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1999)
Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: combining decision procedures. J. Symb. Comput. 21(2), 211–243 (1996)
Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 445–532. Elsevier and MIT Press (2001)
Colmerauer, A.: An introduction to Prolog III. Commun. ACM 33(7), 69–90 (1990)
Dabrowski, R., Plandowski, W.: On word equations in one variable. Algorithmica 60(4), 819–828 (2011)
Diekert, V., Jez, A., Plandowski, W.: Finding all solutions of equations in free groups and monoids with involution. Inf. Comput. 251, 263–286 (2016)
Guttag, J.V., Horowitz, E., Musser, D.R.: Abstract data types and software validation. Commun. ACM 21(12), 1048–1064 (1978)
Ganesh, V., Minnes, M., Solar-Lezama, A., Rinard, M.: Word equations with length constraints: what’s decidable? In: Biere, A., Nahir, A., Vos, T. (eds.) HVC 2012. LNCS, vol. 7857, pp. 209–226. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39611-3_21
Hibbs, P.: Unification modulo common list functions. Doctoral Dissertation. University at Albany–SUNY (2015)
Kapur, D.: Towards a theory for abstract data types. Doctoral Dissertation. Massachusetts Institute of Technology (1980)
Kapur, D., Musser, D.R.: Proof by consistency. Artif. Intell. 31(2), 125–157 (1987)
Karhumäki, J.: Combinatorics on Words: A New Challenging Topic, p. 12. Turku Centre for Computer Science, Turku (2004)
Liang, T., Tsiskaridze, N., Reynolds, A., Tinelli, C., Barrett, C.: A decision procedure for regular membership and length constraints over unbounded strings. In: Lutz, C., Ranise, S. (eds.) FroCoS 2015. LNCS, vol. 9322, pp. 135–150. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24246-0_9
Lin, A.W., Majumdar, R.: Quadratic word equations with length constraints, counter systems, and Presburger arithmetic with divisibility. arXiv preprint arXiv:1805.06701 (2018)
Morita, K.: Universality of a reversible two-counter machine. Theoret. Comput. Sci. 168(2), 303–320 (1996)
Musser, D.R.: Abstract data type specification in the AFFIRM system. IEEE Trans. Softw. Eng. 6(1), 24–32 (1980)
Musser, D.R.: On proving inductive properties of abstract data types. In: Proceedings of the Seventh Annual ACM Symposium on Principles of Programming Languages (POPL), pp. 154–162 (1980)
Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245–257 (1979)
Oppen, D.C.: Reasoning about recursively defined data structures. J. ACM 27(3), 403–411 (1980)
Plandowski, W.: An efficient algorithm for solving word equations. In: Proceedings of the ACM Symposium on the Theory of Computing, pp. 467–476 (2006)
Robson, J.M., Diekert, V.: On quadratic word equations. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 217–226. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49116-3_20
Shostak, R.E.: Deciding combinations of theories. J. ACM 31(1), 1–12 (1984)
Schulz, K.U.: On existential theories of list concatenation. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 294–308. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0022264
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Anantharaman, S., Hibbs, P., Narendran, P., Rusinowitch, M. (2019). Unification Modulo Lists with Reverse Relation with Certain Word Equations. In: Fontaine, P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science(), vol 11716. Springer, Cham. https://doi.org/10.1007/978-3-030-29436-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-29436-6_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29435-9
Online ISBN: 978-3-030-29436-6
eBook Packages: Computer ScienceComputer Science (R0)