Nonaxiomatisability of equivalences over finite state processes

Annals of Pure and Applied Logic

Volumn 90, Issue 1-3, 1997, Pages 163-191

  Sewell, Peter ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Behavioural equivalences; Equational logic; Nonaxiomatisability; Process algebra; Regular expressions

Indexed keywords

EID: 0031574519     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-0072(97)00036-5     Document Type: Article

References (34)

1. L. Aceto, W. Fokkink, R. van Glabbeek, A. Ingólfsdóttir, Axiomatizing prefix iteration with silent steps, Inform. and Comput. 127 (1) (1996) 26-40.
2. L. Aceto, W.J. Fokkink, A. Ingólfsdóttir, A menagerie of non-finitely based process semantics over BPA*: from ready simulation semantics to completed traces, Research Report RS-96-23, BRICS, Department of Mathematics and Computer Science, Aalborg University, July 1996.
3. L. Aceto, A. Ingólfsdóttir, A complete equational axiomatization for prefix iteration with silent steps, Research Report RS-95-5, BRICS (Basic Research in Computer Science, Center of the Danish Research Foundation), Department of Mathematics and Computer Science, Aalborg University, January 1995.
4. K.B. Arkhangelskii, P.V. Gorshkov, Implicational axioms for the algebra of regular languages, Doklady Akad. Nauk USSR, Ser A 10 (1987) 67-69. (in Russian).
5. J.A. Bergstra, I. Bethke, A. Ponse, Process algebra with iteration and nesting, Comput. J. 37 (4) (1994) 243-258. Also as University of Amsterdam Programming Research Group report P9314.
6. S.L. Bloom, Z. Ésik, Equational axioms for regular sets, Math. Struct. Comput. Sci. 3 (1993) 1-24.
7. S.L. Bloom, Z. Ésik, Iteration Theories: The Equational Logic of Iterative Processes, EATCS Monographs on Theoretical Computer Science, Springer, Berlin, 1993.
8. S.L. Bloom, Z. Ésik, Iteration algebras of finite state process behaviors, Manuscript, February 1994.
9. S.L. Bloom, Z. Ésik, D. Taubner, Iteration theories of synchronization trees, Inform. and Comput. 102 (1) (1993).
10. M. Boffa, Une remarque sur les systèmes complets d'identités rationelles, Theoret. Inform. Appl. 24 (4) (1990) 419-423.
11. J.H. Conway, J.H. Conway, Regular Algebra and Finite Machines, Chapman & Hall, London, 1971.
12. I.M. Copi, C.C. Elgot, J.B. Wright, Realization of events by logical nets, J. ACM 5 (2) (1958) 181-196.
13. W.J. Fokkink, A complete equational axiomatisation for prefix iteration, Inform. Process. Lett. 52 (6) (1994) 333-337. Also as CWI report CS-R9415.
14. W. Fokkink, H. Zantema, Basic process algebra with iteration: completeness of its equational axioms, Comput. J. 37 (4) (1994) 259-267, Also as CWI report CS-R9368.
15. C.A.R. Hoare, Communicating Sequential Processes, Series in Computer Science, Prentice-Hall, Englewood Cliffs, NJ, 1985.
16. S.C. Kleene, Representation of events in nerve nets and finite automata, in: C.E. Shannon, J. McCarthy (Eds.), Automata Studies, Princeton University Press, Princeton, 1956, pp. 3-41. Ann. Math. Studies 34.
17. D. Kozen, A completeness theorem for Kleene algebras and the algebra of regular events, Inform. and Comput. 110 (1994) 366-390. Also in LICS '91.
18. D. Krob, Complete systems of B-rational identities, Theoret. Comput. Sci. 89 (1991) 207-343.
19. R. Milner, A complete inference system for a class of regular behaviours, J. Comput. System Sci. 28 (3) (1984) 439-466.
20. R. Milner, A complete axiomatisation for observational congruence of finite state behaviours, Inform. and Comput. 81 (1989) 227-247.
21. F. Moller, Axioms for Concurrency, Ph.D. Thesis, University of Edinburgh, 1989.
22. F. Nielson, The typed λ-calculus with first-class processes, in: Proc. PARLE '89, Lecture Notes in Computer Science, vol. 366, Springer, Berlin, 1989.
23. D.M.R. Park, Concurrency and automata on infinite sequences, in: Proc. 5th G.I. Conf., Lecture Notes in Computer Science, vol. 104, Springer, Berlin, 1981.
24. A. Rabinovich, A complete axiomatisation for trace congruence of finite state behaviors, in: S. Brookes, M. Main, A. Melton, M. Mislove, D. Schmidt (Eds.), Proc. Mathematical Foundations of Programming Semantics (IX), Lecture Notes in Computer Science, vol. 802, Springer, Berlin, 1993, pp. 530-543.
25. V.N. Redko, On defining relations for the algebra of regular events, Ukrain. Mat. Zh. 16 (1964) 120-126 (in Russian).
26. A. Salomaa, Two complete axiom systems for the algebra of regular events, J. ACM 13 (1) (1966) 158-169.
27. D. Sangiorgi, Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms, Ph.D. Thesis, University of Edinburgh, 1993.
28. P.M. Sewell, Bisimulation is not finitely (first-order) equationally axiomatisable, in: Proc. 9th IEEE Symp. on Logic in Computer Science, IEEE, New York, 1994, pp. 62-70.
29. P.M. Sewell, The Algebra of Finite State Processes, Ph.D. Thesis, University of Edinburgh, 1995, Dept. of Computer Science Technical Report CST-118-95, also published as LFCS-95-328.
30. R.J. van Glabbeek, The linear time-branching time spectrum (extended abstract), in: J.C.M. Baeten, J.W. Klop (Eds.), Proc. CONCUR'90, Theories of Concurrency: Unification and Extension, Amsterdam, August 1990, Lecture Notes in Computer Science, vol. 458, Springer, Berlin, 1990, pp. 278-297.
31. R.J. van Glabbeek, A complete axiomatization for branching bisimulation congruence of finite-state behaviours, in: A.M. Borzyszkowski, S. Sokołowski (Eds.), Proc. 18th Internat. Symp. on Mathematical Foundations of Computer Science, MFCS '93, Gdansk, Poland, August/September 1993, Lecture Notes in Computer Science, vol. 711, Springer, Berlin, 1993, pp. 473-484.
32. R.J. van Glabbeek, Divergence bisimulation, Personal communication, 1993.
33. J.L.M. Vrancken, The algebra of communicating processes with empty process, Technical Report FVI 86-01, University of Amsterdam, Department of Computer Science, 1986. A later version appeared in Theoret Comput. Sci. 177 (2) (1997) 287-328.
34. Yanov, See [11, p. 108]