Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-26T20:54:06.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Well (and Better) Quasi-Ordered Transition Systems

Published online by Cambridge University Press:  15 January 2014

Parosh Aziz Abdulla
Parosh Aziz Abdulla*
Affiliation:
Department of Information Technology, Uppsala University, P.O. Box 337, 751 05 Uppsala, Sweden E-mail: parosh@it.uu.se
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we give a step by step introduction to the theory of well quasi-ordered transition systems. The framework combines two concepts, namely (i) transition systems which are monotonic wrt. a well-quasi ordering; and (ii) a scheme for symbolic backward reachability analysis. We describe several models with infinite-state spaces, which can be analyzed within the framework, e.g., Petri nets, lossy channel systems, timed automata, timed Petri nets, and multiset rewriting systems. We will also present better quasi-ordered transition systems which allow the design of efficient symbolic representations of infinite sets of states.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 4 , December 2010 , pp. 457 - 515
Copyright
Copyright © Association for Symbolic Logic 2010

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

REFERENCES

[1] Abdulla, P. A., Čerāns, K., Jonsson, B., and Tsay, Y.-K., General decidability theorems for infinite-state systems, Proceedings of the LICS '96, 11th IEEE International Symposium on Logic in Computer Science, 1996, pp. 313–321.Google Scholar
[2] Abdulla, P. A., Algorithmic analysis of programs with well quasi-ordered domains, Information and Computation, vol. 160 (2000), pp. 109–127.Google Scholar
[3] Abdulla, P. A. and Delzanno, G., On the coverability problem for constrained multiset rewriting, Proceedings of the AVIS'06, 5th International Workshop on on Automated Verification of Infinite-State Systems, 2006.Google Scholar
[4] Abdulla, P. A. and Jonsson, B., Verifying programswith unreliable channels, Proceedings of the LICS '93, 8th IEEE International Symposium on Logic in Computer Science, 1993, pp. 160–170.Google Scholar
[5] Abdulla, P. A. and Jonsson, B., Verifying programs with unreliable channels, Information and Computation, vol. 127 (1996), no. 2, pp. 91–101.CrossRefGoogle Scholar
[6] Abdulla, P. A. and Jonsson, B., Verifying networks of timed processes, Proceedings of the TACAS '98, 4th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (Steffen, Bernhard, editor), Lecture Notes in Computer Science, vol. 1384, 1998, pp. 298–312.Google Scholar
[7] Abdulla, P. A. and Jonsson, B., Ensuring completeness of symbolic verification methods for infinite-state systems, Theoretical Computer Science, vol. 256 (2001), pp. 145–167.CrossRefGoogle Scholar
[8] Abdulla, P. A. and Jonsson, B., Model checking of systems with many identical timed processes, Theoretical Computer Science, vol. 290 (2003), no. 1, pp. 241–264.CrossRefGoogle Scholar
[9] Abdulla, P. A. and Nylén, A., Better is better than well: On efficient verification of infinite-state systems, Proceedings of the LICS '00, 16th IEEE International Symposium on Logic in Computer Science, 2000, pp. 132–140.Google Scholar
[10] Abdulla, P. A. and Nylén, A., Timed Petri nets and BQOs, Proceedings on the ICATPN'2001: 22nd International Conference on Application and Theory of Petri Nets, Lecture Notes in Computer Science, vol. 2075, 2001, pp. 53–70.Google Scholar
[11] Alur, R., Courcoubetis, C., and Dill, D., Model-checking for real-time systems, Proceedings of the LICS '90, 5th IEEE International Symposium on Logic in Computer Science, 1990, pp. 414–425.Google Scholar
[12] Alur, R. and Dill, D., A theory of timed automata, Theoretical Computer Science, vol. 126 (1994), pp. 183–235.Google Scholar
[13] Bartlett, K., Scantlebury, R., and Wilkinson, P., A note on reliable full-duplex transmissions over half duplex lines, Communications of the ACM, vol. 12 (1969), no. 5, pp. 260–261.CrossRefGoogle Scholar
[14] Biere, A., Cimatti, A., Clarke, E. M., and Zhu, Y., Symbolic model checking without BDDs, Proceedings of the TACAS '99, 5th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, 1999.Google Scholar
[15] Bouyer, P., Forward analysis of updatable timed automata, Formal Methods in System Design, vol. 24 (2004), no. 3, pp. 281–320.Google Scholar
[16] Bryant, R. E., Graph-based algorithms for boolean function manipulation, IEEE Transactions on Computers, vol. C-35 (1986), no. 8, pp. 677–691.Google Scholar
[17] Burch, J. R., Clarke, E. M., McMillan, K. L., and Dill, D. L., Symbolic model checking: 1020 states and beyond, Information and Computation, vol. 98 (1992), pp. 142–170.CrossRefGoogle Scholar
[18] Čerāns, K., Deciding properties of integral relational automata, Proceedings of the ICALP '94, 21st International Colloquium on Automata, Languages, and Programming (Abiteboul, and Shamir, , editors), Lecture Notes in Computer Science, vol. 820, Springer Verlag, 1994, pp. 35–46.Google Scholar
[19] Clarke, E. M., Emerson, E. A., and Sistla, A. P., Automatic verification of finite-state concurrent systems using temporal logic specification, ACM Transactions on Programming Languages and Systems, vol. 8 (1986), no. 2, pp. 244–263.CrossRefGoogle Scholar
[20] Cormen, T., Leiserson, C., Rivest, R., and Stein, C., Introduction to algorithms, MIT Press, McGraw-Hill, 2001.Google Scholar
[21] Delzanno, G., Automatic verification of cache coherence protocols, Proceedings of the 12th International Conference on Computer Aided Verification (Emerson, and Sistla, , editors), Lecture Notes in Computer Science, vol. 1855, Springer Verlag, 2000, pp. 53–68.Google Scholar
[22] Dickson, L. E., Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors, American Journal of Mathematics, vol. 35 (1913), pp. 413–422.Google Scholar
[23] Esparza, J., Finkel, A., and Mayr, R., On the verification of broadcast protocols, Proceedings of the LICS '99, 14th IEEE International Symposium on Logic in Computer Science, 1999.Google Scholar
[24] Finkel, A., A generalization of the procedure of Karp and Miller to well structured transition systems, Proceedings of the ICALP '87, 14th International Colloquium on Automata, Languages, and Programming, 1987, pp. 499–508.Google Scholar
[25] Finkel, A., Decidability of the termination problem for completely specified protocols, Distributed Computing, vol. 7 (1994), no. 3, pp. 129–135.Google Scholar
[26] Finkel, A. and Schnoebelen, Ph., Well-structured transition systems everywhere!, Theoretical Computer Science, vol. 256 (2001), no. 1–2, pp. 63–92.CrossRefGoogle Scholar
[27] Higman, G., Ordering by divisibility in abstract algebras, Proceedings of the London Mathematical Society (3), vol. 2 (1952), no. 7, pp. 326–336.Google Scholar
[28] Jančar, P., ω2-well quasi-orderings and reachability analysis, Technical Report 158, Department of Computing Systems, Uppsala University, 1999.Google Scholar
[29] Larsen, K.G., Pettersson, P., and Yi, W., UPPAAL in a nutshell, International Journal on Software Tools for Technology Transfer, vol. 1 (1997), no. 1–2.CrossRefGoogle Scholar
[30] Lazic, R., Newcomb, T., Ouaknine, J., Roscoe, A. W., and Worrell, J., Nets with tokens which carry data, Fundamentals of Information, (2008), no. 3, pp. 251–274.Google Scholar
[31] Marcone, A., Fine and axiomatic analysis of the quasi-orderings on (q), Technical Report 17/99/RR, Rapporto di Ricerca del Dipartimento di Matematica e Informatica dell'Università di Udine, 1999.Google Scholar
[32] McMillan, K. L., Symbolic model checking, Kluwer Academic Publishers, 1993.Google Scholar
[33] Milner, E. C., Basic wqo- and bqo-theory, Graphs and orders (Rival, I., editor), D. Reidel Publishing Company, 1985, pp. 487–502.Google Scholar
[34] Niebert, P., Mahfoudh, M., Asarin, E., Bozga, M., Jain, N., and Maler, O., Verification of timed automata via satisfiability checking, FTRTFT'02, 7th International Symposium on Formal Techniques in Real-Time and Fault Tolerant Systems, vol. 2469, 2002, pp. 225–243.Google Scholar
[35] Pouzet, M., Applications of well quasi-orderings and better quasi-orderings, Graphs and orders (Rival, I., editor), D. Reidel Publishing Company, 1985, pp. 503–519.CrossRefGoogle Scholar
[36] Queille, J. P. and Sifakis, J., Specification and verification of concurrent systems in Cesar, 5th International Symposium on Programming, Turin, Lecture Notes in Computer Science, vol. 137, Springer Verlag, 1982, pp. 337–352.Google Scholar
[37] Revesz, P., Introduction to constraint databases, Springer, 2002.Google Scholar
[38] Yovine, S., Kronos: A verification tool for real-time systems, International Journal on Software Tools for Technology Transfer, vol. 1 (1997), no. 1–2.CrossRefGoogle Scholar