Computing the average parallelism in trace monoids

Discrete Mathematics

Volumn 273, Issue 1-3, 2003, Pages 131-162

  Krob, Daniel ^a   Mairesse, Jean ^a   Michos, Ioannis ^a  

^a UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Automata and formal languages; Cartier Foata normal form; Generating series; Performance evaluation; Trace monoids

Indexed keywords

ALGEBRA; FUNCTIONS; PROBABILITY DISTRIBUTIONS; SET THEORY;

CARTIER-FOATA DECOMPOSITIONS; TRACE MONOIDS;

GRAPH THEORY;

EID: 0345376923     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(03)00233-4     Document Type: Conference Paper

References (33)

1. Berstel J., Reutenauer C. Rational Series and their Languages. 1988;Springer, Berlin.
2. A. Bertoni, M. Goldwurm, B. Palano, A fast parallel algorithm for the speed-up problem of traces, in: Proceedings of the workshop on Trace Theory and Code Parallelization, Vol. 263-00 in Rapporto Interno, Univ. degli Studi di Milano, 2000, pp. 29-36.
3. Blondel V., Gaubert S., Tsitsiklis J. Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard. IEEE Trans. Autom. Control. 45(9):2000;1762-1765.
4. Brémaud P. Markov chains: Gibbs fields, Monte Carlo simulation, and queues. Texts in Applied Mathematics. Vol. 31:1999;Springer, Berlin.
5. M. Brilman, Evaluation de Performances d'une Classe de Systèmes de Ressources Partagées, Ph.D. Thesis, Univ. Joseph Fourier, Grenoble I, 1996.
6. Brilman M., Vincent J.M. On the estimation of the throughput for a class of stochastic resources sharing systems. Math. Oper. Res. 23(2):1998;305-321.
7. k) Portugal. Math. 21(5):1962;201-207.
8. Cartier P., Foata D. Problèmes combinatoires de commutation et réarrangements. Lecture Notes in Mathematics. Vol. 85:1969;Springer, Berlin.
9. C. Cérin, A. Petit, Speedup of recognizable trace languages, in: Proceedings of the MFCS 93, Lecture Notes in Computer Science, Vol. 711, Springer, Berlin, 1993, pp. 332-341.
10. Cvetković D., Doob M., Sachs H. Spectra of Graphs. Theory and Application. Pure and Applied Mathematics. Vol. 87:1980;Academic Press, Paris.
11. V. Diekert, Y. Métivier, Partial commutation and traces, in: Handbook of Formal Languages, Vol. 3, Springer, Berlin, 1997, pp. 457-533.
12. V. Diekert, G. Rozenberg (Eds.), The Book of Traces, World Scientific, Singapore, 1995.
13. P. Flajolet, R. Sedgewick, The average case analysis of algorithms: complex asymptotics and generating functions, Reseach Report RR-2026, INRIA, Rocquencourt, France, 1993.
14. S. Gaubert, J. Mairesse, Task resource models and (max,+) automata, in: J. Gunawardena (Eds.), Idempotency, Vol. 11, Cambridge University Press, Cambridge, 1998, pp. 133-144.
15. Gaubert S., Mairesse J. Performance evaluation of timed Petri nets using heaps of pieces. Bucholz P., Silva M. Petri Nets and Performance Models (PNPM'99). 1999;158-169 IEEE Computer Society, Silver Spring, MD.
16. Godsil C. Matchings and walks in graphs. J. Graph Theory. 5:1981;285-297.
17. Godsil C. Algebraic Combinatorics. 1993;Chapman & Hall, London.
18. Godsil C., Gutman I. On the theory of the matching polynomial. J. Graph Theory. 5:1981;137-144.
19. Goldwurm M., Santini M. Clique polynomials have a unique root of smallest modulus. Inform. Process. Lett. 75(3):2000;127-132.
20. Graham R., Knuth D., Patashnik O. Concrete Mathematics: a Foundation for Computer Science. 2nd Edition:1994;Addison-Wesley, Reading, MA.
21. Hakim V., Nadal J.-P. Exact results for 2d directed animals on a strip of finite width. J. Phys. A: Math. Gen. 16:1983;L213-L218.
22. A. Jean-Marie, ERS: a tool set for performance evaluation of discrete event systems. http://www-sop.inria.fr/mistral/soft/ers.html.
23. A. Jean-Marie, personal communication, September 2001.
24. Krob D., Mairesse J., Michos I. On the average parallelism in trace monoids. Alt H., Ferreira A. Proceedings of STACS'02, Lecture Notes in Computer Science. 2002;Springer, Berlin.
25. Nadal J.-P., Derrida B., Vannimenus J. Directed lattice animals in 2 dimensions. numerical and exact results J. Phys. 43:1982;1561-1574.
26. Revuz D. Markov Chains. 1975;North-Holland Mathematical Library, North-Holland, Amsterdam.
27. Saheb N. Concurrency measure in commutation monoids. Discrete Appl. Math. 24:1989;223-236.
28. N. Saheb, A. Zemmari, Methods for computing the concurrency degree of commutation monoids, in: Proceedings FPSAC'00, Moscow, Russia, Springer, Berlin, 2000, pp. 731-742.
29. E. Seneta, Non-negative Matrices and Markov Chains, Springer Series in Statistics, Springer, Berlin, 1981.
30. R. Stanley, Enumerative Combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, 1986.
31. Titchmarsh E.C. The Theory of Functions. 2nd Edition:1975;Oxford University Press, Oxford.
32. G.X. Viennot, Heaps of pieces, I: Basic definitions and combinatorial lemmas, in: Labelle, Leroux (Eds.), Combinatoire Énumérative, Lecture Notes in Mathematics, Vol. 1234, Springer, Berlin, 1986, pp. 321-350.
33. Wilf H. Generatingfunctionology. 1990;Academic Press, New York.