Decision procedures for extensions of the theory of arrays

Annals of Mathematics and Artificial Intelligence

Volumn 50, Issue 3-4, 2007, Pages 231-254

  Ghilardi, Silvio ^a   Nicolini, Enrica ^b   Ranise, Silvio ^b   Zucchelli, Daniele ^a,b  

^a UNIVERSITY OF MILAN   (Italy)

^b LORIA   (France)

Author keywords

Combination methods; Constraint satisfiability problems; Decision procedures; Instantiation strategies; Presburger arithmetic; Theory of arrays with extensionality

Indexed keywords

EID: 34548212807     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-007-9078-x     Document Type: Conference Paper

References (27)

1. Armando, A., Bonacina,M.P., Ranise, S., Schulz, S.: On a rewriting approach to satisfiability procedures: extension, combination of theories and an experimental appraisal. In: Proceedings of the 5th International Workshop on Frontiers of Combining Systems (FroCoS'05). LNCS, vol. 3717, pp. 65-80. Springer (2005)
2. Armando, A., Ranise, S., Rusinowitch,M.: A rewriting approach to satisfiability procedures. Inf. Comput. 183(2), 140-164 (2003)
3. Bjørner, N., Stickel, M.E., Uribe, T.E.: A practical integration of first-order reasoning and decision procedures. In: Proceedings of the 14th International Conference on Automated Deduction (CADE'97). LNCS, vol. 1249, pp. 101-115. Springer (1997)
4. Bonacina, M.P., Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Decidability and undecidability results for Nelson-Oppen and rewrite-based decision procedures. In: Proceedings of the 3rd International Joint Conference on Automated Reasoning (IJCAR'06). LNCS, vol. 4130, pp. 513-527. Springer (2006)
5. Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., Ranise, S., van Rossum, P., Sebastiani, R.: Efficient theory combination via boolean search. Inf. Comput. 204(10), 1493-1525 (2006)
6. Bradley, A.R., Manna, Z., Sipma, H.B.: What's decidable about arrays? In: Proceedings of the 7th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI'06). LNCS, vol. 3855, pp. 427-442. Springer (2006)
7. Brodnik, A., Carlsson, S., Demaine, E.D., Munro, J.I., Sedgewick, R.: Resizable arrays in optimal time and space. In: Proceedings of 6th International Workshop on Algorithms and Data Structures (WADS'99). LNCS, vol. 1663, pp. 37-48. Springer (1999)
8. Déharbe, D., Ranise, S.: Light-weight theorem proving for debugging and verifying units of code. In: Proceedings of the 1st International Conference on Software Engineering and Formal Methods (SEFM'03), pp. 220-228. IEEE Computer Society (2003)
9. Downey, P.J., Sethi, R.: Assignment commands with array references. J. ACM 25(4), 652-666 (1978)
10. Enderton, H.B.: A Mathematical Introduction to Logic. Academic, New York (1972)
11. Gallier, J.H.: Logic for Computer Science: Foundations of Automatic Theorem Proving. Harper & Row (1986)
12. Ganzinger, H., Korovin, K.: Integrating equational reasoning in instantiation-based theorem proving. In: Proceedings of the 18th International Workshop on Computer Science in Logic (CSL'04). LNCS, vol. 3210, pp. 71-84. Springer (2004)
13. Ghilardi, S.: Model-theoretic methods in combined constraint satisfiability. J. Autom. Reason. 33(3-4), 221-249 (2004)
14. Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Deciding extension of the theory of arrays by integrating decision procedures and instantiation strategies. Rapporto Interno DSI 309-06, Università degli Studi di Milano, Milano (Italy) (2006) Available at http://homes.dsi.unimi.it/~zucchell/ publications/techreport/GhiNiRaZu-RI309-06.pdf
15. Jaffar, J.: Presburger arithmetic with array segments. Inf. Process. Lett. 12(2), 79-82 (1981)
16. Mateti, P.: A decision procedure for the correctness of a class of programs. J. ACM 28(2), 215-232 (1981)
17. McCarthy, J.: Towards a mathematical theory of computation. In: Proceedings of IFIP Congress, pp. 21-28 (1962)
18. McPeak, S., Necula, G.: Data structures specification via local equality axioms. In: Proceedings of the 17th International Conference on Computer Aided Verification (CAV'05). LNCS, vol. 3576, pp. 476-490. Springer (2005)
19. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245-257 (1979)
20. Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, chapter 7, pp. 371-443. Elsevier Science (2001)
21. Reynolds, J.C.: Reasoning about arrays. Commun. ACM 22(5), 290-299 (1979)
22. Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of the 17th IEEE Symposium on Logic in Computer Science (LICS'02), pp. 55-74. IEEE Computer Society (2002)
23. Rusinowitch, M.: Démonstration Automatique (Techniques de réécriture). InterEditions (1989)
24. Schrijver, A.: Theory of Linear and Integer Programming. Wiley (1986)
25. Stump, A., Barrett, C.W., Dill, D.L., Levitt, J.: A decision procedure for an extensional theory of arrays. In: Proceedings of the 16th IEEE Symposium on Logic in Computer Science (LICS'01). pp. 29-37. IEEE Computer Society (2001)
26. Suzuki, N., Jefferson, D.R.: Verification decidability of Presburger array programs. J. ACM 27(1), 191-205 (1980)
27. van Dalen, D.: Logic and Structure, 2nd edn. Springer (1989)