F. , R. , F. , and R. Lab, F (pour Forbidden), est l'ensemble des actions interdites, Il contient les lettres a qui n'apparaissent dans aucune séquence de P aths(C , C). R (pour Required), est l'ensemble des actions nécessaires

F. [. Le-langage-de-toutes-les-séquences-qui-ne-contiennent-aucune-lettre-de and R. Au-moins-une-occurrence-de-chaque-lettre-de, Il est facile de voir que les langages représentés par [F 1 , R 1 ] et [F 2 , R 2 ] ont une intersection vide si et seulement si F 1 ? R 2 = ? ou R 1 ?. Dans la figure 7.3 nous pouvons utiliser cette abstraction pour déduire qu'aucune configuration ayant n 1 et m 2 comme points de contrôle n'est accessible : L'action a est nécessaire pour accéderaccéder`accéderà n 1 , mais interdite si nous voulons arriveràarriver

Q. =. Soient, ?. =. , ?. , R. , and Q. =. , Nous appliquons les r` egles (? 1 )?(? 5 ) et nous obtenons le système de contraintes suivant : 1. l(q n 0 , s 1 ) l(q m 0 , s) ? l

L. Contraintes, et (3) sont obtenues par (? 4 ) puisque ||(q n 0 , q m 0 ) ? q n 0 ||m 0 ? ? et ||(s, s) ? s, ||(s 1 , s) ? s 1 , et ||(s, s 1 ) ? s 1 sont des r

L. Contraintes, et (8) sont obtenues en appliquant (? 5 ) aux r` egles R 1

. [. Bibliographie, A. Abdulla, A. Annichini, and . Bouajjani, Symbolic Verification of Lossy Channel Systems : Application to the Bounded Retransmission Protocol, TACAS'99. LNCS 1579, 1999.

R. Alur, R. K. Brayton, T. A. Henzinger, S. Qadeer, S. K. Abdulla et al., Partial-order reduction in symbolic state space exploration On-the-fly Analysis of Systems with Unbounded, Lossy Fifo Channels, Computer Aided Verification CAV'98, pp.340-351, 1997.

P. A. Abdulla, A. Bouajjani, B. Jonsson, and M. Nilsson, Handling Global Conditions in Parametrized System Verification, Lecture Notes in Computer Science, vol.1633, pp.134-150, 1999.
DOI : 10.1007/3-540-48683-6_14

A. Annichini, A. Bouajjani, and M. Sighireanu, TReX: A Tool for Reachability Analysis of Complex Systems, Computer Aided Verification, pp.368-372, 2001.
DOI : 10.1007/3-540-44585-4_34

URL : https://hal.archives-ouvertes.fr/hal-00110460

P. Abdulla, K. Cerans, B. Jonsson, Y. Alur, C. Courcoubetis et al., General decidability theorems for infinite-state systems Model-checking for real-time systems The algorithmic analysis of hybrid systems A Theory of Timed Automata Undecidable verification problems for programs with unreliable channels, Proc. of the 11th Annual IEEE Symposium on Logic in Computer Science 5th Symp. on Logic in Computer Science (LICS 90)AJ98] Parosh Aziz Abdulla and Bengt Jonsson. Verifying Networks of Timed Processes TACAS'98, pp.313-321, 1990.

P. A. Abdulla, B. Jonsson, P. Mahata, and J. , Regular tree model-checking d'Orso. Regular modelchecking made simple and efficient, 14th Intern. Conf. on Computer Aided Verification (CAV'02) Proceedings 13th International Conference on Concurrency Theory (CONCUR), volume 2421 of Lecture Notes in Computer Science, pp.116-130, 2002.
DOI : 10.1007/3-540-45657-0_47

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.7184

D. [. Apt and . Kozen, Limits for automatic verification of finite-state concurrent systems, Information Processing Letters, vol.22, issue.6, pp.307-309, 1986.
DOI : 10.1016/0020-0190(86)90071-2

M. [. Abdulla and . Kindahl, Decidability of simulation and bisimulation between lossy channel systems and finite state systems, Proc. Intern. Conf. on Concurrency Theory (CONCUR'95). LNCS 962, 1995.
DOI : 10.1007/3-540-60218-6_25

O. [. Asarin, A. Maler, and . Pnueli, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, pp.35-65, 1995.
DOI : 10.1016/0304-3975(94)00228-B

T. Arons, A. Pnueli, S. Ruah, J. Xu, and L. Zuck, Parameterized Verification with Automatically Computed Inductive Assertions?, Lecture Notes in Computer Science, vol.2102, p.221, 2001.
DOI : 10.1007/3-540-44585-4_19

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.7408

K. Baukus, S. Bensalem, Y. Lakhnech, and K. Stahl, Abstracting WS1S Systems to Verify Parameterized Networks, Tools and Algorithms for Construction and Analysis of Systems, pp.188-203, 2000.
DOI : 10.1007/3-540-46419-0_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.6696

B. [. Blieberger, B. Burgstaller, and . Scholz, Symbolic Data Flow Analysis for Detecting Deadlocks in Ada Tasking Programs, Proc. of the Ada-Europe International Conference on Reliable Software Technologies, 2000.
DOI : 10.1007/10722060_21

]. J. Bcm-+-92, E. M. Burch, K. Clarke, D. Mcmillan, L. Dill et al., Symbolic model-checking : 10 20 states and beyond, Information and Computation, vol.98, issue.2, pp.142-170, 1992.

S. [. Ball, S. K. Chaki, and . Rajamani, Parameterized Verification of Multithreaded Software Libraries, TACAS 2001, 2001.
DOI : 10.1007/3-540-45319-9_12

J. [. Burkart and . Esparza, More infinite results, In EATCS Bulletin, vol.62, pp.138-159, 1997.

J. [. Bouajjani, O. Esparza, and . Maler, Reachability analysis of pushdown automata: Application to model-checking, CONCUR'97, 1997.
DOI : 10.1007/3-540-63141-0_10

]. A. Bet03a, J. Bouajjani, T. Esparza, and . Touili, A generic approach to the static analysis of concurrent programs with procedures, Proceedings of the 30th ACM SIPGPLAN-SIGACT on Principles of Programming Languages, p.3, 2003.

A. Bouajjani, J. Esparza, and T. Touili, A generic approach to the static analysis of concurrent programs with procedures, International Journal of Foundations of Computer Science, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00161114

A. Bouajjani, J. Esparza, and T. Touili, Abstract Reachability Analysis of Programs with Dynamic Creation of Threads and Procedure Calls, 2003.

P. [. Boigelot and . Godefroid, Symbolic verification of communication protocols with infinite state spaces using QDDs, CAV'96, 1996.
DOI : 10.1007/3-540-61474-5_53

P. [. Boigelot, B. Godefroid, P. Willems, and . Wolper, The power of QDDs, SAS'97, 1997.

P. [. Bouajjani and . Habermehl, Symbolic Reachability Analysis of FIFO- Channel Systems with Nonregular Sets of Configurations, ICALP'97, 1997.

P. [. Bouajjani, T. Habermehl, and . Vojnar, Verification of Parametric Concurrent Systems with Prioritized FIFO Resource Management, Proceedings of CONCUR'03, 2003.
DOI : 10.1007/978-3-540-45187-7_11

URL : https://hal.archives-ouvertes.fr/hal-00159537

A. Bouajjani, B. Jonsson, M. Nilsson, and T. Touili, Regular Model Checking, 12th Intern. Conf. on Computer Aided Verification (CAV'00)
DOI : 10.1007/10722167_31

URL : https://hal.archives-ouvertes.fr/hal-00159512

J. [. Bergstra and . Klop, Algebra of communicating processes with abstraction, Theoretical Computer Science, vol.37, 1985.
DOI : 10.1016/0304-3975(85)90088-X

M. [. Bruggemann-klein, D. Murata, and . Wood, Regular tree and regular hedge languages over unranked alphabets, 2001.

J. Bengtsson, K. G. Larsen, F. Larsson, P. Pettersson, and W. Yi, UPPAAL -a tool suite for automatic verification of real-time systems, Hybrid Systems, pp.232-243, 1995.

A. [. Boigelot, P. Legay, and . Wolper, Iterating Transducers in the Large, 15th Intern. Conf. on Computer Aided Verification (CAV'03). LNCS, 2003.
DOI : 10.1007/978-3-540-45069-6_24

A. [. Bouajjani, T. Muscholl, and . Touili, Permutation Rewriting and Algorithmic Verification, Proc. 17th Symp. on Logic in Computer Science (LICS'01, 2001.
DOI : 10.1109/lics.2001.932515

URL : https://hal.archives-ouvertes.fr/hal-00161120

]. A. Bou01 and . Bouajjani, Languages, Rewriting systems, and Verification of Infinte- State Systems, ICALP'01, 2001.

Y. [. Burkart and . Quemener, Model-checking of infinite graphs defined by graph grammars, Proc. 4th Int. Workshop Verification of Infinite State Systems (INFINITY'96), 1996.

S. [. Ball and . Rajamani, Bebop: A Symbolic Model Checker for Boolean Programs, SPIN00 : SPIN Workshop, pp.113-130, 2000.
DOI : 10.1007/10722468_7

W. S. Brained, Tree generating regular systems, Information and Control, vol.14, issue.2, pp.217-231, 1969.
DOI : 10.1016/S0019-9958(69)90065-5

R. E. Bryant, Symbolic Boolean manipulation with ordered binary-decision diagrams, ACM Computing Surveys, vol.24, issue.3, pp.293-318, 1992.
DOI : 10.1145/136035.136043

URL : http://akebono.stanford.edu/users/nanni/courses/EE318/bryant92.pdf

B. [. Burkart and . Steffen, Composition, decomposition, and modelchecking of pushdown processes, Nordic Journal of Computing, vol.2, issue.2, pp.89-125, 1995.

B. [. Burkart and . Steffen, Model-checking the full modal mu-calculus for infinite sequential processes, Proc. ICALP'97, pp.419-429, 1997.

T. [. Bouajjani and . Touili, Extrapolating Tree Transformations, 14th Intern. Conf. on Computer Aided Verification (CAV'02). LNCS, 2002.
DOI : 10.1007/3-540-45657-0_46

URL : https://hal.archives-ouvertes.fr/hal-00161115

A. Bouajjani and T. Touili, Effective Reachability Sets of Process Rewrite Systems, 2003.

A. Bouajjani and T. Touili, Reachability Analysis of Process Rewrite Systems, FSTTCS'03, 2003.
DOI : 10.1007/978-3-540-24597-1_7

URL : https://hal.archives-ouvertes.fr/hal-00161112

P. [. Boigelot and . Wolper, Symbolic verification with periodic sets, CAV'94, 1994.
DOI : 10.1007/3-540-58179-0_43

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.6568

[. Boigelot and P. Wolper, Verifying systems with infinite but regular state spaces, Proc. 10th Int. Conf. on Computer Aided Verification , CAV'98, pp.88-97, 1998.

[. Boigelot and P. Wolper, On the construction of automata from linear arithmetic constraints, TACAS'00, pp.1-19, 2000.

D. Caucal, On the regular structure of prefix rewriting, Theoretical Computer Science, vol.106, issue.1, pp.61-86, 1992.
DOI : 10.1016/0304-3975(92)90278-N

R. [. Cousot and . Cousot, Static Determination of Dynamic Properties of Recursive Procedures, IFIP Conf. on Formal Description of Programming Concepts, 1977.

V. [. Comon, J. Cortier, and . Mitchell, Tree Automata with One Memory, Set Constraints, and Ping-Pong Protocols, ICALP'2001, 2001.
DOI : 10.1007/3-540-48224-5_56

J. L. Coquidé, M. Dauchet, R. Gilleron, and S. Vágvölgyi, Bottom-up tree pushdown automata and rewrite systems, Theoretical Computer Science, vol.127, issue.1, pp.69-98, 1994.
DOI : 10.1007/3-540-53904-2_104

E. M. Clarke, E. A. Emerson, and E. Sistla, Automatic verification of finite state concurrent system using temporal logic specifications, Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '83, 1983.
DOI : 10.1145/567067.567080

A. [. Cécé, S. P. Finkel, and . Iyer, Unreliable Channels Are Easier to Verify Than Perfect Channels, Information and Computation, vol.124, issue.1, pp.20-31, 1996.
DOI : 10.1006/inco.1996.0003

O. [. Clarke, S. Grumberg, and . Jha, Verifying parameterized networks using abstraction and regular languages, Lecture Notes in Computer Science, vol.962, pp.395-407, 1995.
DOI : 10.1007/3-540-60218-6_30

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.5751

P. Cousot and N. Halbwachs, Automatic discovery of linear restraints among variables of a program, Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '78, 1978.
DOI : 10.1145/512760.512770

G. [. Coquand and . Huet, The calculus of construction. Formal Methods in System Design, 1988.

]. S. Chr93 and . Christensen, Decidability and Decomposition in Process Algebras, 1993.

]. T. Col02 and . Colcombet, Rewriting in the partial algebra of typed terms modulo ac, Electronic Notes in Theoretical Computer Science, 2002.

]. J. Cor92 and . Corbett, Automated Formal Analysis Methods for Concurrent and Real-Time Software, 1992.

L. [. Delzanno, J. Van-begin, and . Raskin, Attacking symbolic state explosion in parametrized verification, CAV'01, 2001.

L. [. Delzanno, J. Van-begin, and . Raskin, Towards the Automated Verification of Multithreaded Java Programs, 2002.
DOI : 10.1007/3-540-46002-0_13

E. [. Diekert and . Rozenberg, The Book of Traces, World Scientific, 1995.
DOI : 10.1142/2563

]. D. Dil89 and . Dill, Timing assumptions and verification of finite-state concurrent systems, Proc. of the International Workshop on Automartic Verification Methods for Finite State Systems, pp.197-212, 1989.

[. Dams, Y. Lakhnech, and M. Steffen, Iterating transducers, 13th Intern. Conf. on Computer Aided Verification (CAV'01)
DOI : 10.1007/3-540-44585-4_27

A. [. Daws, S. Olivero, S. Tripakis, and . Yovine, The tool Kronos, Hybrid Systems III : Verification and Control, pp.208-219, 1995.
DOI : 10.1007/BFb0020947

M. [. Duesterwald and . Soffa, Concurrency analysis in the presence of procedures using a data-flow framework, Proceedings of the symposium on Testing, analysis, and verification , TAV4, pp.36-48, 1991.
DOI : 10.1145/120807.120811

M. Dauchet and S. Tison, The theory of ground rewrite systems is decidable, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science, pp.242-248, 1990.
DOI : 10.1109/LICS.1990.113750

J. Esparza, D. Hansel, P. Rossmanith, and S. Schwoon, Efficient Algorithms for Model Checking Pushdown Systems, CAV'00, 2000.
DOI : 10.1007/10722167_20

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.3784

J. [. Esparza and . Knoop, An Automata-Theoretic Approach to Interprocedural Data-Flow Analysis, Proc of Foundations of Software Science and Computation Structure, FoSSaCS'99, volume 1578 of Lecture Notes in Computer Science, 1999.
DOI : 10.1007/3-540-49019-1_2

[. Emerson and V. Kahlon, Model-checking large-scale and parametrized resource allocation systems, TACAS'02, 2002.
DOI : 10.1007/3-540-46002-0_18

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.948

J. Esparza and S. Melzer, Checking system properties via integer programming, European Symposium on Programming, pp.250-264, 1996.

]. E. Eme90 and . Emerson, Temporal and Modal Logic, pp.996-1072, 1990.

M. [. Esparza and . Nielsen, Decidability issues for Petri nets -a survey, Bulletin of the EATCS, vol.52, pp.85-107, 1994.
DOI : 10.7146/brics.v1i8.21662

URL : http://ojs.statsbiblioteket.dk/index.php/brics/article/download/21662/19099

K. [. Emerson and . Namjoshi, Reasoning about rings, Proc. 22th ACM Symposium on Principles of Programming Languages, POPL'95, 1995.
DOI : 10.1145/199448.199468

K. [. Emerson and . Namjoshi, Automatic verification of parametrized synchronous systems, Proc. 8th International Conference on Computer Aided Verification, CAV'96, 1996.

J. Engelfriet, Bottom-up and top-down tree transformations??? a comparison, Mathematical Systems Theory, pp.198-231, 1975.
DOI : 10.1007/BF01704020

URL : http://purl.utwente.nl/publications/85444

A. [. Esparza and . Podelski, Efficient algorithms for pre* and post* on interprocedural parallel flow graphs, Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages , POPL '00, pp.1-11, 2000.
DOI : 10.1145/325694.325697

S. [. Esparza and . Schwoon, A BDD-Based Model Checker for Recursive Programs, Proc. of CAV'01, number 2102 in Lecture Notes in Computer Science, pp.324-336, 2001.
DOI : 10.1007/3-540-44585-4_30

J. Esparza, Decidability of model checking for infinite-state concurrent systems, Acta Informatica, vol.34, issue.2, pp.85-107, 1997.
DOI : 10.1007/s002360050074

J. Esparza, Petri nets, commutative context-free grammars, and basic parallel processes, Fundamenta Informaticae, pp.13-25, 1997.
DOI : 10.1007/3-540-60249-6_54

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.2829

]. J. Esp02 and . Esparza, Grammars as processes, Formal and Natural Computing, 2002.

J. Fernandez, C. Jard, T. Jeron, and L. Mounier, on-the-fly " verification of finite transition systems, Formal Methods in System Design, 1992.
URL : https://hal.archives-ouvertes.fr/inria-00074812

J. [. Finkel and . Leroux, How to Compose Presburger-Accelerations: Applications to Broadcast Protocols, FSTTCS'02, 2002.
DOI : 10.1007/3-540-36206-1_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.9119

H. [. Fribourg and . Olsen, Reachability sets of parametrized rings as regular languages, Infinity'97, 1997.

D. Fisman and A. Pnueli, Beyond Regular Model Checking, Lecture Notes in Computer Science, vol.2245, p.156, 2001.
DOI : 10.1007/3-540-45294-X_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.8730

M. [. Fischer and . Rabin, Super-Exponential Complexity of Presburger Arithmetic, Proceedings of the Symposium on the Complexity of Real Computation Processes, 1993.
DOI : 10.1007/978-3-7091-9459-1_5

J. [. Finkel, M. Raskin, L. Samuelides, and . Van-begin, Monotonic Extensions of Petri Nets, Proc. 4th Int. Workshop Verification of Infinite State Systems (INFINI- TY'2002), 2002.
DOI : 10.1016/S1571-0661(04)80535-8

URL : https://hal.archives-ouvertes.fr/hal-00158709

B. [. Finkel, P. Willems, and . Wolper, A Direct Symbolic Approach to Model Checking Pushdown Systems, Infinity'97, 1997.

A. [. Gilleron and . Deruyver, The reachability problem for ground TRS and some extensions, Proc. Int. Joint Conf. Theory and Practice of Software Development (TAPSOFT'89), pp.227-243, 1989.
URL : https://hal.archives-ouvertes.fr/inria-00538873

]. R. Gil91 and . Gilleron, Decision problems for term rewriting systems and recognizable tree languages, Proc. of STACS'91, pp.148-159, 1991.

F. [. Genet and . Klay, Rewriting for Cryptographic Protocol Verification, Proceedings 17th International Conference on Automated Deduction, 2000.
DOI : 10.1007/10721959_21

URL : https://hal.archives-ouvertes.fr/inria-00072731

C. [. Graf and . Loiseaux, A tool for symbolic program verification and abstraction, Proc. 5th Int. Conf. on Computer Aided Verification, CAV'97, pp.71-84, 1993.
DOI : 10.1007/3-540-56922-7_7

. [. Goubault-larrecq, A Method for Automatic Cryptographic Protocol Verification, 15th IPDPS 2000 Workshops, 2000.
DOI : 10.1007/3-540-45591-4_134

]. P. God96 and . Godefroid, Partial-order methods for the verification of concurrent systems -An approach to the state-explosion problem, Lecture Notes in Computer Science, 1032.

E. [. Ginsburg and . Spanier, Semigroups, Presburger formulas, and languages, Pacific Journal of Mathematics, vol.16, issue.2, pp.285-296, 1966.
DOI : 10.2140/pjm.1966.16.285

S. M. German and A. P. Sistla, Reasoning about systems with many processes, Journal of the ACM, vol.39, issue.3, pp.675-735, 1992.
DOI : 10.1145/146637.146681

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.2632

P. [. Godefroid and . Wolper, Using partial orders for the efficient verification of deadlock freedom and safety properties, Formal Methods in System Design, pp.149-164, 1993.

G. [. Gribomont and . Zenner, Automated verification of Szymanski's algorithm, TACAS'98, pp.424-438, 1998.
DOI : 10.1007/BFb0054187

]. P. Hab98 and . Habermehl, Sur la vérification des systèmes infinis, 1998.

]. M. Har78 and . Harrison, Introduction to Formal Language Theory, 1978.

A. Thomas, P. Henzinger, H. Ho, and . Wong-toi, HYTECH : A model checker for hybrid systems, International Journal on Software Tools for Technology Transfer, vol.1, issue.12, pp.110-122, 1997.

M. [. Hirshfeld, F. Jerrum, and . Moller, A polynomial algorithm for deciding bisimulation of normed context free processes, technical report, 1994.

M. [. Hirshfeld, F. Jerrum, and . Moller, A polynomial-time algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes, Mathematical Structures in Computer Science, vol.832, issue.03, 1996.
DOI : 10.1016/0020-0190(92)90142-I

D. [. Hopkins and . Kozen, Parikh's theorem in commutative Kleene algebra, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158), 1999.
DOI : 10.1109/LICS.1999.782634

G. [. Huet, C. Kahn, and . Paulin-mohring, The coq proof assistant -a tutorial, version 6.1, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00069967

P. [. Henzinger, A. Kopke, P. Puri, and . Varaiya, What's decidable about hybrid automata ?, Proc. of the 27th Annual Symposium on Theory of Computing, pp.373-382, 1995.
DOI : 10.1006/jcss.1998.1581

URL : http://doi.org/10.1006/jcss.1998.1581

D. [. Halbwachs, P. Lesens, and . Raymond, Automatic Verification of parametrized linear networks of processes, 24th ACM Symposium on Principles of Programming Languages, POPL'97, 1997.

X. [. Henzinger, J. Nicollin, S. Sifakis, and . Yovine, Symbolic model checking for real-time systems, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science, pp.193-244, 1994.
DOI : 10.1109/LICS.1992.185551

]. G. Hol94 and . Holzmann, Basic SPIN Manual, 1994.

E. John, J. Hopcroft, and . Pansiot, On the reachability problem for 5-dimensional vector addition systems, In Journal of Computer and System Sciences, vol.8, pp.135-159, 1979.

N. Halbwachs, P. Raymond, and Y. E. Proy, Verification of linear hybrid systems by means of convex approximations, International Symposium on Static Analysis (SAS'94). LNCS 1579, 1994.
DOI : 10.1007/3-540-58485-4_43

L. [. Howell, H. C. Rosier, and . Yen, A taxonomy of fairness and temporal logic problems for petri nets, Theoretical Computer Science, vol.82, 1991.

J. [. Hopcroft and . Ullman, Introduction to automata Theory, languages, and computation, 1979.
DOI : 10.1145/568438.568455

]. P. Jan90 and . Jancar, Decidability of a temporal logic problem for petri nets, Theoretical Computer Science, p.74, 1990.

]. P. Jan97 and . Jancar, Decidability Questions for Bisimilarity of Petri Nets and Some Related Problems, 1997.

[. Fernandez, H. Garavel, A. Kerbrat, L. Mounier, R. Mateescu et al., CADP a protocol validation and verification toolbox, Proceedings of the Eighth International Conference on Computer Aided Verification CAV, pp.437-440, 1996.
DOI : 10.1007/3-540-61474-5_97

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.6237

T. [. Jard and . Jeron, On-line model-checking for finite linear temporal logic. International Workshop on Automatic Verification Methods for Finite State Systems, 1989.
URL : https://hal.archives-ouvertes.fr/inria-00075517

N. [. Jensen and . Lynch, A proof of burns N-process mutual exclusion algorithm using abstraction, TACAS'98, pp.409-423, 1998.
DOI : 10.1007/BFb0054186

F. [. Jancar and . Moller, Checking regular properties of petri nets, Proc. 6th Int. Conf. Concurrency Theory (CONCUR'95), 1995.

M. [. Jonsson and . Nilsson, Transitive Closures of Regular Relations for Verifying Infinite-State Systems, 6th TACAS (TACAS 00). to appear in LNCS, 2000.
DOI : 10.1007/3-540-46419-0_16

T. [. Jha, S. Reps, and . Schwoon, Weighted Pushdown Systems and their application to Interprocedural Dataflow Analysis, Proc. of the 10th International Symposium on Static Analysis, 2003.

K. [. Kurshan and . Mcmillan, A structural induction theorem for processes, ACM Symp. on Principles of Distributed Computing, pp.239-247, 1989.

. Kmm-+-97-]-y, O. Kesten, M. Maler, A. Marcus, E. Pnueli et al., Symbolic model checking with rich assertional languages, Proc. CAV'97, pp.424-435, 1997.

]. J. Kno98 and . Knoop, Optimal interprocedural program optimization : A new framework and its applications, LNCS Tutorial, 1428.

]. D. Koz83 and . Kozen, Results on the Propositional µ-calculus, Theoretical Computer Science, vol.27, 1983.

]. D. Lon93 and . Long, Model-checking, abstraction, and compositional verification, 1993.

. [. Lugiez, . Ph, and . Schnoebelen, The regular viewpoint on PA-processes
URL : https://hal.archives-ouvertes.fr/inria-00073287

]. D. Lug03 and . Lugiez, Counting and equality constraints for multitree automata, 2003.

]. L. Mau99 and . Mauborgne, Representation of Sets of Trees for Abstract Interpretation, 1999.

]. R. May98 and . Mayr, Decidability and Complexity of Model Checking Problems for Infinite-State Systems, 1998.

]. K. Mcm93 and . Mcmillan, Symbolic Model-Checking : an Approach to the State- Explosion Problem, Kluwer, 1993.

]. K. Mcm98 and . Mcmillan, Getting started with smv. User's manual, 1998.

D. [. Melton, C. N. Dill, U. Ip, and . Stern, Murphi annotated reference manual, release 3.0, 1996.

]. N. Mer91 and . Mercouroff, An algorithm for analyzing communicating processes, Mathematical Foundations of Programming Semantics, pp.312-337, 1991.

]. R. Mil80 and . Milner, A Calculus of Communicating Systems, LNCS, vol.92, 1980.

]. F. Mol96 and . Moller, Infinite results, Proceedings of CONCUR'96, 1996.

]. D. Mon02 and . Monniaux, Abstracting cryptographic protocols with tree automata, Science of Computer Programming, 2002.

A. [. Manna and . Pnueli, An Exercise in the Verification of Multi-Process Programs, Beauty in Our Business, pp.289-301, 1990.
DOI : 10.1007/978-1-4612-4476-9_34

M. [. Mayr and . Rusinowitch, Reachability is decidable for ground ac rewrite systems, Proc. Int. Workshop Verification of Infinite State Systems (INFINITY'98, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00098437

]. A. Mus96 and . Muscholl, ¨ Uber die Erkennbarkeit unendlicher Spuren, 1996.

G. Naumovich and G. Avrunin, A conservative data flow algorithm for detecting all pairs of statement that may happen in parallel, Proceedings of the ACM SIGSOFT International Symposium on Foundations of Software Engineeringhol?a proof assistant for higher-order logic, pp.24-34, 1998.

F. Oehl, G. Cécé, O. Kouchnarenko, D. [. Sinclair, J. Owre et al., Automatic Approximation for the Verification of Cryptographic Protocols PPS : a prototype verification system The temporal logic of programs Data Flow Analysis of Communicating Finite State Machines, Proceedings of the International Conference on Formal Aspects of SecurityOpp78] D. Oppen. A 2 2 2 n upper bound on the complexity of Presburger arithmetic Journal of Computer and System Sciences., number 16 Proc. of the 11th Conf. on Automated Deduction Proc. of the 18th IEEE Symposium on the Foundations of Computer Science (FOCS-77)Pre29] M. Presburger. uber die Vollstandingen einer gewissen Systems der Arithmetik ganzer Zahlen welchem die Addition als einzige Operation hervortritt . Comptes Rendus du premier Congr'es des Math'ematiciens des Pays slaves, pp.323-332, 1929.

A. Pnueli, S. Ruah, L. Zuckps00, ]. A. Pnueli, and E. Shahar, Automatic deductive verification with invisible invariants Liveness and acceleration in parametrized verification, TACAS'01 12th Intern. Conf. on Computer Aided Verification (CAV'00), 2001.

[. Pin and P. Weil, Polynomial closure and unambiguous product, Theory of Computing Systems, pp.383-422, 1997.
DOI : 10.1007/bf02679467

URL : https://hal.archives-ouvertes.fr/hal-01248158

D. A. Peled, T. Wilke, P. Wolper, [. Queille, and J. Sifakis, An algorithmic approach for checking closure properties of temporal logic specifications and omega-regular languages Specification and Verification of Concurrent Systems in Cesar Context-sensitive synchronization-sensitive analysis is undecidable, Proc. Intern. Symposium on ProgrammingTOPLAS), pp.183-203416, 1982.

H. G. Ricesg89-]-z, O. Stadler, ]. N. Grumbergsor93, S. Shankar, J. M. Owre et al., Analysis of multithreaded programs Deterministic tree pushdown automata and monadic tree rewriting systems Data flow analysis is model checking of abstract interpretation Moped -a model-checker for pushdown systems Network grammars, communication behaviors and automatic verification The PVS proof checker : A reference manual (draft) Program analysis as model checking of abstract interpretations Constraint-based inter-procedural analysis of parallel programs Constraint-based inter-procedural analysis of parallel programs Data fow analysis as model checking A lattice-theoretical fixpoint theorem and its applications A general-purpose algorithm for analyzing concurrent programs Right-linear finite path overlapping term rewriting systems effectively preserve recognizability, Proc. of the 8th International Symposium on Static Analysis Proceedings of POPL'98 Proc. Workshop on Automatic Verification Methods for Finite State Systems Proceedings of SAS'98 Programming Languages and Systems (ESOP'2000), volume 1782 of Electronic Notes in Theoretical Computer Science TACS'91Sti96] C. Stirling. Modal and temporal logic for processes. Logics for ConcurrencyTho82] W. Thomas. Classifying regular events in symbolic logic. Journal of Computer and System SciencesTou01] T. Touili. Widening Techniques for Regular Model Checking 1st vepas workshop of Electronic Notes in Theoretical Computer Science, pp.25-59367, 1953.

A. Valmari, Stubborn sets for reduced state space generation, Lecture Notes in Computer Science, vol.483, pp.491-515, 1991.
DOI : 10.1007/3-540-53863-1_36

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.3089

. Y. Vw86-]-m, P. Vardi, and . Wolper, An Automata-Theoretic Approach to Automatic Program Verification, Proc. 2nd Symp. on Logic in Computer Science (LICS'86, 1986.

I. Walukiewicz, Pushdown Processes: Games and Model Checking, 8th Intern. Conf. on Computer Aided Verification (CAV'96), pp.62-74
DOI : 10.7146/brics.v3i54.20057

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.4162

V. [. Wolper and . Lovinfosse, Verifying properties of large sets of processes with network invariants, Workshop on Automatic Verification Methods for Finite State Systems, 1989.
DOI : 10.1007/3-540-52148-8_6

]. P. Wol86 and . Wolper, Expressing interesting properties of programs in propositional temporal logic, Proc. of the 13th ACM Symposium on Principles of Programming Languages, pp.184-193, 1986.

]. P. Wol93 and . Wolper, Temporal logic can be more expressive, Formal Methods in System Design, pp.149-164, 1993.

E. Yahav, Verifying safety properties of concurrent Java programs using 3-valued logic, ACM SIGPLAN Notices, vol.36, issue.3, pp.27-40, 2001.
DOI : 10.1145/373243.360206

]. S. Yov98 and . Yovine, Model-checking timed automata, Lecture Notes in Computer Science, vol.1494, pp.114-153, 1998.