Abstract
We investigate the issue of reducing the verification problem of multi-stack machines to the one for single-stack machines. For instance, elegant (and practically efficient) algorithms for bounded-context switch analysis of multi-pushdown systems have been recently defined based on reductions to the reachability problem of (single-stack) pushdown systems [10,18]. In this paper, we extend this view to both bounded-phase visibly pushdown automata (BVMPA) [16] and ordered multi-pushdown automata (OMPA) [1] by showing that each of their emptiness problem can be reduced to the one for a class of single-stack machines. For these reductions, we introduce effective generalized pushdown automata (EGPA) where operations on stacks are (1) pop the top symbol of the stack, and (2) push a word in some (effectively) given set of words L over the stack alphabet, assuming that L is in some class of languages for which checking whether L intersects regular languages is decidable. We show that the automata-based saturation procedure for computing the set of predecessors in standard pushdown automata can be extended to prove that for EGPA too the set of all predecessors of a regular set of configurations is an effectively constructible regular set. Our reductions from OMPA and BVMPA to EGPA, together with the reachability analysis procedure for EGPA, allow to provide conceptually simple algorithms for checking the emptiness problem for each of these models, and to significantly simplify the proofs for their 2ETIME upper bounds (matching their lower-bounds).
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Atig, M.F., Bollig, B., Habermehl, P.: Emptiness of multi-pushdown automata is 2ETIME-complete. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 121–133. Springer, Heidelberg (2008)
Atig, M.F., Bouajjani, A., Touili, T.: On the reachability analysis of acyclic networks of pushdown systems. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 356–371. Springer, Heidelberg (2008)
Bouajjani, A., Esparza, J.: Rewriting models of boolean programs. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 136–150. Springer, Heidelberg (2006)
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)
Bouajjani, A., Müller-Olm, M., Touili, T.: Regular symbolic analysis of dynamic networks of pushdown systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 473–487. Springer, Heidelberg (2005)
Breveglieri, L., Cherubini, A., Citrini, C., Crespi Reghizzi, S.: Multi-push-down languages and grammars. International Journal of Foundations of Computer Science 7(3), 253–292 (1996)
Caucal, D.: On infinite transition graphs having a decidable monadic theory. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 194–205. Springer, Heidelberg (1996)
Esparza, J., Knoop, J.: An automata-theoretic approach to interprocedural data-flow analysis. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 14–30. Springer, Heidelberg (1999)
Kahlon, V.: Boundedness vs. unboundedness of lock chains: Characterizing decidability of pairwise cfl-reachability for threads communicating via locks. In: LICS, pp. 27–36. IEEE Computer Society, Los Alamitos (2009)
Lal, A., Reps, T.W.: Reducing concurrent analysis under a context bound to sequential analysis. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 37–51. Springer, Heidelberg (2008)
Qadeer, S.: The case for context-bounded verification of concurrent programs. In: Havelund, K., Majumdar, R., Palsberg, J. (eds.) SPIN 2008. LNCS, vol. 5156, pp. 3–6. Springer, Heidelberg (2008)
Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)
Ramalingam, G.: Context-sensitive synchronization-sensitive analysis is undecidable. ACM Trans. Program. Lang. Syst. 22(2), 416–430 (2000)
Reps, T.W., Schwoon, S., Jha, S.: Weighted pushdown systems and their application to interprocedural dataflow analysis. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 189–213. Springer, Heidelberg (2003)
Seth, A.: Global reachability in bounded phase multi-stack pushdown systems. In: CAV 2010. LNCS. Springer, Heidelberg (2010)
La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: Proceedings of LICS, pp. 161–170. IEEE, Los Alamitos (2007)
La Torre, S., Madhusudan, P., Parlato, G.: An infinite automation characterization of double exponential time. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 33–48. Springer, Heidelberg (2008)
La Torre, S., Madhusudan, P., Parlato, G.: Reducing context-bounded concurrent reachability to sequential reachability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 477–492. Springer, Heidelberg (2009)
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Atig, M.F. (2010). From Multi to Single Stack Automata. In: Gastin, P., Laroussinie, F. (eds) CONCUR 2010 - Concurrency Theory. CONCUR 2010. Lecture Notes in Computer Science, vol 6269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15375-4_9
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DOI: https://doi.org/10.1007/978-3-642-15375-4_9
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