Series-parallel languages and the bounded-width property

Theoretical Computer Science

Volumn 237, Issue 1-2, 2000, Pages 347-380

  Lodaya, K ^a   Weil, P ^b  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Automata; Bounded parallel width; Fork and join; N free posets; Process hierarchy; Rational expressions; Recognizability; Series parallel poset languages

Indexed keywords

EID: 0000673486     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(00)00031-1     Document Type: Article

References (28)

1. S. Bloom, Z. Ésik, Free shuffle algebras in language varieties, Theoret. Comput. Sci. 163 (1996) 55-98.
2. J.R. Büchi, in: D. Siefkes (Ed.), Finite Automata, their Algebras and Grammars: Towards a Theory of Formal Expressions, Springer, Berlin, 1989.
3. B. Courcelle, On recognizable sets and tree automata, in: M. Nivat, H. Ait-Kaci (Eds.), Resolution of equations in Algebraic Structures, Vol. 1, Academic Press, New York, 1989, pp. 93-126.
4. B. Courcelle, Graph rewriting: an algebraic and logical approach, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, Vol. B, Elsevier, Amsterdam, 1990, pp. 193-242.
5. V. Diekert, G. Rozenberg, The Book of Traces, World Scientific, Singapore, 1995.
6. J. Doner, Tree acceptors and some of their applications, J. Comput. Systems Sci. 4 (1970) 406-451.
7. M. Droste, P. Gastin, Asynchronous cellular automata for pomsets without auto-concurrency, in: U. Montanari, V. Sassone (Eds.), CONCUR, Pisa, Lecture Notes in Computer Science, Vol. 1119, Springer, Berlin, 1996, pp. 627-638.
8. S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press, New York, 1974.
9. V.K. Garg, M.T. Ragunath, Concurrent regular expressions and their relationship to Petri nets, Theoret. Comput. Sci. 96 (1992) 285-304.
10. F. Gécseg, M. Steinby, Tree Automata, Akadémiai Kiadó, Budapest, 1984.
11. J.L. Gischer, The equational theory of pomsets, Theoret. Comput. Sci. 61 (1988) 199-224.
12. J. Grabowski, On partial languages, Fund. Inform. IV (1981) 427-498.
13. J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979.
14. G. Lallement, Semigroups and Combinatorial Applications, Wiley, New York, 1979.
15. K. Lodaya, P. Weil, Rationality in algebras with a series operation, IMSc Rep. 99/11/39, Institute of Mathematical Sciences, Feb 2000 (Available as http://www.imsc.ernet.in/~kamal/ssig.ps.gz).
16. A. Mazurkiewicz, Concurrent program schemes and their interpretations, DAIMI Rep. PB 78, Aarhus University, 1977.
17. J. Mezei, J. Wright, Algebraic automata and context-free sets, Inform, and Control 11 (1967) 3-29.
18. M. Nielsen, G.D. Plotkin, G. Winskel, Petri nets, event structures and domains, Part I, Theoret. Comput. Sci. 13 (1981) 85-108.
19. E. Ochmański, Regular behaviour of concurrent systems, Bull. EATCS 27 (1985) 56-67.
20. J.-E. Pin, Syntactic semigroups, in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Language Theory, Vol. I, Springer, Berlin, 1997, pp. 679-746.
21. J.-E. Pin, P. Weil, A Reiterman theorem for pseudovarieties of finite first-order structures, Algebra Univ. 35 (1996) 577-595.
22. V. Pratt, Modelling concurrency with partial orders, Internat. J. Parallel Prog. 15 (1) (1986) 33-71.
23. W. Reisig, G. Rozenberg (Eds.), in: Lectures on Petri Nets (2 Vols), Lecture Notes in Computer Science, Vol. 1491-2, Springer, Berlin, 1998.
24. M. Steinby, Some algebraic aspects of recognizability and rationality, in: F. Gécseg (Ed.), Fundamentals of Computation Theory, Szeged, Lecture Notes in Computer Science, Vol. 117, Springer, Berlin, 1981, pp. 360-372.
25. J.W. Thatcher, J.B. Wright, Generalized finite automata with an application to a decision problem of second order logic, Math. Systems Theory 2 (1968) 57-82.
26. J. Valdes, R.E. Tarjan, E.L. Lawler, The recognition of series-parallel digraphs, SIAM J. Comput. 11 (1981) 298-313.
27. J. Winkowski, Algebras of partial sequences - a tool to deal with concurrency, in: M. Karpinski (Ed.), Fundamentals of Computation Theory, Poznań-Kórnik, Lecture Notes in Computer Science, Vol. 56, Springer, Berlin, 1977, pp. 187-196.
28. W. Zielonka, Notes on finite asynchronous automata, RAIRO Inform. Théorique Appl. 21 (1987) 99-135.