Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T11:54:34.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficiency of automata in semi-commutation verification techniques

Published online by Cambridge University Press:  25 September 2007

Gérard Cécé ,
Pierre-Cyrille Héam  and
Yann Mainier
Gérard Cécé
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; [email protected]; [email protected]; [email protected]
Pierre-Cyrille Héam
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; [email protected]; [email protected]; [email protected]
Yann Mainier
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; [email protected]; [email protected]; [email protected]
Get access

Abstract

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages L – called APC – of the form UjL0,jL1,jL2,j...Lkj,j, where the union is finite and each Li,j is either a single symbol or a language of the form B* with B a subset of the alphabet, is closed under all semi-commutation relations R. Moreover a recursive algorithm on the regular expressions was given to compute R*(L). This paper provides a new approach, based on automata, for the same problem. Our approach produces a simpler and more efficient algorithm which furthermore works for a larger class of regular languages closed under union, intersection, semi-commutation relations and conjugacy. The existence of this new class, PolC, answers the open question proposed in the paper of Bouajjani et al.

Keywords

Regular model checkingverificationparametric systemssemi-commutations
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 197 - 215
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdulla, P.A., Bouajjani, A. and Jonsson, B., On-the-fly analysis of systems with unbounded, lossy FIFO channels, in CAV'98. Lect. Notes Comput. Sci. 1427 (1998) 305–322. CrossRef
Abdulla, P., Annichini, A. and Bouajjani, A., Algorithmic verification of lossy channel systems: An appliction to the bounded retransmission protocol, in TACAS'99. Lect. Notes Comput. Sci. 1579 (1999) 208–222. CrossRef
Abdulla, P.A., Jonsson, B., Nilsson, M. and d'Orso, J., Algorithmic improvements in regular model checking, in CAV'03. Lect. Notes Comput. Sci. 2725 (2003) 236–248. CrossRef
J. Berstel, Transductions and Context-Free Languages. B.G. Teubner, Stuttgart (1979).
B. Boigelot and P. Godefroid, Symbolic verification of communication protocols with infinite state spaces using QDDs, in Proc. of 8th CAV (August), USA 1102 (1996) 1–12.
Boigelot, B. and Wolper, P., Verifying systems with infinite but regular state spaces. In CAV'98. Lect. Notes Comput. Sci. 1427 (1998) 88–97.
A. Bouajjani, A. Muscholl and T. Touili, Permutation rewriting and algorithmic verification, in LICS'01. IEEE Comput. Soc. (2001) 399–408.
J.A. Brzozowski, Hierarchies of aperiodic languages, 10 (1976) 33–49.
J.A. Brzozowski and I. Simon, Characterizations of locally testable languages. 4 (1973) 243–271.
G. Cécé, P.-C. Héam and Y. Mainier, Clôture transitives de semi-commutations et model-checking régulier, in AFADL'04 (2004).
V. Diekert and Y. Métivier, Partial commutation and traces, in Handbook on Formal Languages, volume III, edited by G. Rozenberg and A. Salomaa, Springer, Berlin-Heidelberg-New York (1997).
V. Diekert and G. Rozenberg, Ed. Book of Traces. World Scientific, Singapore (1995).
Esik, Z. and Simon, I., Modeling literal morphisms by shuffle. Semigroup Forum 56 (1998) 225–227. CrossRef
Godefroid, P. and Wolper, P., A partial approach to model checking. Inform. Comput. 110 (1994) 305–326. CrossRef
A. Cano Gomez and J.-E. Pin, On a conjecture of schnoebelen, in DLT'03. (2003).
A. Cano Gomez and J.-E. Pin, Shuffle on positive varieties of languages. 312 (2004) 433–461.
G. Guaiana, A. Restivo and S. Salemi, On the trace product and some families of languages closed under partial commutations. 9 (2004) 61–79.
P.-C. Héam, Some complexity results for polynomial rational expressions. 299 (2003).
J. Hopcroft and J. Ullman, Introduction to automata theory, languages, and computation. Addison-Wesley (1980).
X. Leroy, D. Doligez, J. Garrigue, D. Rémy, and J. Vouillon, The Objective Caml system, release 3.06. Inria, 2002.
D. Lugiez and Ph. Schnoebelen, The regular viewpoint on pa-processes, in 9th Int. Conf. Concurrency Theory (CONCUR'98). . 1466 (1998).
J.-F. Perrot, Variété de langages et opérations. 7 (1978) 197–210.
J.-E. Pin, Varieties of formal languages. Foundations of Computer Science (1984).
Pin, J.-E. and Weil, P., Polynomial closure and unambiguous product. Theor. Comput. Syst. 30 (1997) 1–39. CrossRef
Schnoeboelen, Ph., Decomposable regular languages and the shuffle operator. EATCS Bull. 67 (1999) 283–289.
H. Straubing, Finite semigroups varieties of the form V*D. 36 (1985) 53–94.
P. Tesson and D. Thérien, Diamonds are forever: the variety da, in International Conference on Semigroups, Algorithms, Automata and Languages (2002).
W. Thomas, Classifying regular events in symbolic logic. 25 (1982) 360–375.
D. Thérien, Classification of finite monoids: the language approach. 14 (1981) 195–208.
T. Touili. Regular model checking using widening techniques, in 1st Vepas Workshop, volume 50 of Electronic Notes in TCS (2001).