A finite axiomatization of nondeterministic regular expressions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 447-465.
@article{ITA_1999__33_4-5_447_0,
     author = {Corradini, Flavio and De Nicola, Rocco and Labella, Anna},
     title = {A finite axiomatization of nondeterministic regular expressions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {447--465},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4-5},
     year = {1999},
     zbl = {0945.68122},
     mrnumber = {1748666},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1999__33_4-5_447_0/}
}
TY  - JOUR
AU  - Corradini, Flavio
AU  - De Nicola, Rocco
AU  - Labella, Anna
TI  - A finite axiomatization of nondeterministic regular expressions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 1999
DA  - 1999///
SP  - 447
EP  - 465
VL  - 33
IS  - 4-5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_1999__33_4-5_447_0/
UR  - https://zbmath.org/?q=an%3A0945.68122
UR  - https://www.ams.org/mathscinet-getitem?mr=1748666
LA  - en
ID  - ITA_1999__33_4-5_447_0
ER  - 
Corradini, Flavio; De Nicola, Rocco; Labella, Anna. A finite axiomatization of nondeterministic regular expressions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 447-465. http://www.numdam.org/item/ITA_1999__33_4-5_447_0/

[1] L. Aceto and W. Fokkink, An Equational Axiomatization for multi-exit iteration. Inform. and Comput. 134 (1997) 121-158. | MR 1468880 | Zbl 0881.68069

[2] L. Aceto, W. Fokkink, R. Van Glabbeek and A. Ingólfsdóttir, Axiomatizing prefix iteration with silent steps. Inform. and Comput 127 (1996) 26-40. | MR 1394553 | Zbl 0855.68030

[3] L. Aceto, W. Fokkink and A. Ingólfsdóttir, A managerie of non-finitely based process semantics over BPA*: From ready simulation to completed traces. Research Report, BRICS, RS-96-23 (1996).

[4] J. C. M. Baeten and J. A. Bergstra, Process Algebra with a Zero Object, in Proc. of Concu'90. Springer, Lecture Notes in Comput Sci. 458 (1990) 83-98. | MR 1082157

[5] L. Bernatsky, S. L. Bloom, Z. Ésik and Gh. Stefanescu, Equational theories of relations and regular sets, in Proc. of Words, Languages and Combinatorics, Kyoto, 1992. Word Scientific, (1994) 40-48. | MR 1351278 | Zbl 0874.08002

[6] S. L. Bloom and Z. Ésik, Iteration Algebras of Finite State Process Behaviours. Manuscript.

[7] S. L. Bloom, Z. Ésik and D. Taubner, Iteration theories of synchronization trees. Inform. and Comput. 102 (1993) 1-55. | MR 1201904 | Zbl 0780.68088

[8] M. Boffa, Une remarque sur les systèmes complets d'identités rationelles. Theoret. Informatics Appl. 24 (1990) 419-423. | Numdam | MR 1079723 | Zbl 0701.68059

[9] J. H. Conway, Regular Algebra and Finite Machines. Chapman and Hall, London (1971). | Zbl 0231.94041

[10] F. Corradini, R. De Nicola and A. Labella, Fully Abstract Models for Nondeterministic Regular Expressions, in Proc. of Concur'95. Springer Verlag, Lecture Notes in Comput. Sci. 962 (1995) 130-144.

[11] F. Corradini, R. De Nicola and A. Labella, Models of Nondeterministic Regular Expressions. J. Comput. System Sci., to appear. | MR 1726770 | Zbl 0958.68090

[12] R. De Nicola and A. Labella, Tree Morphisms and Bisimulations, in Proc. of MFCS'98 Workshop on Concurrency. Elsevier, Amsterdam, Electron. Notes Theoret. Comput. Sci. 18 (1998). | MR 1672349

[13] R. De Nicola and A. Labella, A Completeness Theorem for Nondeterministic Kleene Algebras, in Proc. of MFCS'94. Springer, Lecture Notes in Comput. Sci. 841 (1994) 536-545.

[14] W. Fokkink, A complete equational axiomatization for prefix iteration. Inform. Process. Lett. 52 (1994) 333-337. | MR 1307752 | Zbl 0938.68697

[15] W. Fokkink, On the completeness of the Equations for the Kleene Star in Bisimulation, in Proc. of AMAST'96. Springer, Lecture Notes in Comput. Sci. 1101 (1996) 180-194. | MR 1480695 | Zbl 0886.03032

[16] W. Fokkink, Axiomatizations for the perpetual loop in Process Algebras, in Proc. of ICALP'97. Springer, Lecture Notes in Comput. Sci. 1256 (1997) 571-581. | MR 1616217

[17] W. Fokkink and H. Zantema, Basic process algebra with iteration: Completeness of its equational axioms. Comput. J. 37 (1994) 259-267.

[18] C. A. R. Hoare, Communicating Sequential Processes. Prentice Hall (1989). | Zbl 0637.68007

[19] S. C. Kleene, Representation of Events in Nerve Nets and Finite Automata, in Automata Studies, Shannon and McCarthy, Ed. Princeton Univ. Pr. (1956) 3-41. | MR 77478

[20] S. Kasangian and A. Labella, Enriched Categorical Semantics for Distributed Calculi. J. Pure Appl. Algebra 83 (1992) 295-321. | MR 1194841 | Zbl 0777.18007

[21] D. Kozen, A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events. Inform. and Comput 110 (1994) 366-390. | MR 1276741 | Zbl 0806.68082

[22] D. Krob, Complete Systems of B-rational identities. Theoret. Comput. Sci. 89 (1991) 207-343. | MR 1133622 | Zbl 0737.68053

[23] W. Kuich and A. Salomaa, Semirings, Automata, Languages. Springer, Berlin, Monogr. Theoret. Comput. Sci. EATCS Ser. 5 (1986). | MR 817983 | Zbl 0582.68002

[24] R. Milner, A Calculus of Communicating Systems. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 94 (1980). | MR 590046 | Zbl 0452.68027

[25] R. Milner, A complete inference System for a class of regular behaviors. J. Comput. System Sci. 28 (1984) 439-466. | MR 752442 | Zbl 0562.68065

[26] R. Milner, Communication and Concurrency. Prentice Hall (1989). | Zbl 0683.68008

[27] R. N. Moll, M. A. Arbib and A. J. Kfoury, An Introduction to Formal Language Theory. Springer-Verlag, Berlin (1987). | MR 956253 | Zbl 0655.68002

[28] D. Park, Concurrency and Automata on Infinite sequences, in Proc. GI. Springer, Lecture Notes in Comput. Sci. 104 (1981) 167-183. | Zbl 0457.68049

[29] B. C. Pierce, Basic Category Theory for Computer Scientists. The MIT Press (1991). | MR 1120026 | Zbl 0875.18001

[30] V. N. Redko, On defining relations for the algebra of regular events (Russian). Ukrain. Mat. Z. 16 (1964) 120-126. | MR 179033

[31] J. Sakarovitch, Kleene's theorem revisited, in Proc. of Trends, techniques, and problems in theoretical computer science. Springer, Lecture Notes in Comput. Sci. 281 (1986) 39-50. | MR 921502 | Zbl 0637.68096

[32] A. Salomaa, Two Complete Axiom Systems for the Algebra of Regular Events. J. ACM 13 (1966) 158-169. | MR 189995 | Zbl 0149.24902

[33] P. Sewell, Bisimulation is not finitely (first order) equationally axiomatisable, in Proc. of LICS'94 (1994).

[34] M. B. Smith and G. D. Piotkin, The category-Theoretic Solution of Recursive Domain Equation. SIAM J. Comput. 11 (1982) 762-783. | MR 677666 | Zbl 0493.68022

[35] D. R. Troeger, Step bisimulation is pomset equivalence on a parallel language without explicit internal choice. Math. Structures Comput. Sci. 3 (1993) 25-62. | MR 1206871 | Zbl 0806.68044