Abstract
We prove that the existence of a coding between two trace monoids is decidable for some families of trace monoids. Decidability heavily depends on the structure of the dependence graphs. The concept of coding is based on the new notion of strong morphism between trace monoids.
This work was partially supported by ESPRIT-BRA Working Group 6317 ASMICS.
Partially supported by ESPRIT-BRA Working Group 6317 ASMICS and Project 40% MURST Algoritmi, Modelli di Calcolo e Strutture Informative.
Partially supported by a C.N.R. fellowship and Cooperation Project C.G.R.I.-C.N.R.S. Théorie des Automates et Applications.
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References
I.J. Aalbersberg, H.J. Hoogeboom, Characterizations of the decidability of some problems for regular trace languages, Math. Systems Theory 22 (1989) 1–19.
I.J. Aalbersberg, G. Rozenberg, Theory of traces, Theoret. Comput. Sci. 60 (1988) 1–82.
A. Apostolico, R. Giancarlo, Pattern matching machine implementation of a fast test for unique decipherability, Information Processing Letters 18 (1984) 155–158.
J. Berstel, D. Perrin, Theory of Codes, Academic Press, New York, 1985.
B. Bollobás, Extremal Graph Theory, Academic Press, New York, 1978.
V. Bruyère, C. De Felice, G. Guaiana, Decidability for coding between trace monoids, in preparation (1993).
R.M. Capocelli, Comments on “Trends in the Theory of Codes” by J. Berstel and D. Perrin, Bull. EATCS 30 (1986) 43–44.
P. Cartier, D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics 85, Springer, Berlin Heidelberg New-York (1969).
C. Choffrut, Free partially commutative monoids, Technical report 86–20, LITP, Université Paris 7 (1986).
M. Chrobak, W. Rytter, Unique decipherability for partially commutative alphabets, Fundamenta Informaticae 10 (1987) 323–336.
R. Cori, Y. Métivier, Recognizable subsets of some partially abelian monoids, Theoret. Comput. Sci. 35 (1985) 241–254.
R. Cori, D. Perrin, Automates et commutations partielles, RAIRO, Inform. Théor. 19 (1985) 21–32.
V. Diekert, Research topics in the theory of free partially commutative monoids, Bulletin of EATCS 40 (1990) 479–491.
V. Diekert, Combinatorics on traces, Lecture Notes in Comput. Sci. 454, Springer, Berlin Heidelberg New-York (1990).
V. Diekert, G. Rozenberg Tracebook, to appear (1993).
C. Duboc, Commutations dans les monoÏdes libres: un cadre théorique pour l'étude du parallélisme, thèse, Université de Rouen (1986).
C. Duboc, On some equations in free partially commutative monoids, Theoret. Comput. Sci. 46 (1986) 159–174.
E. Galvin, J. L. Peterson, A. Silberschatz, Operating System Concept, Addison Wesley Publishing Company, 1991.
L. Lovasz, Normal hypergraphs and the perfect graph conjecture, Discr. Math. 2 (1972) 253–267.
A. Mazurkiewicz, Concurrent program schemes and their interpretations, DAIMI Rep. PB 78, Aarhus University, Aarhus (1977).
A. Mazurkiewicz, Trace theory, in W. Brauer et al. Ed., Petri Nets, applications and relationship to other models of concurrency, Lecture Notes in Comput. Sci. 255 (1987) 279–324.
E. Ochmanski, On morphisms of trace monoids, Proc. STACS 88, Lecture Notes Comput. Sci. 294 (1988) 346–355.
D. Perrin, Partial commutations, Lecture Notes Comput. Sci. 372 (1989) 637–651.
F. P. Preparata, Introduction to Computer Engineering, Harper and Row, New York, 1985.
M. Rodeh, A fast test for unique decipherability based on suffix trees, IEEE Trans. Inform. Theory 28 (1982) 648–651.
A.A. Sardinas, C.W. Patterson, A necessary and sufficient condition for the unique decomposition of coded messages, IRE Internat. Conv. Rec. 8 (1953) 104–108.
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© 1994 Springer-Verlag Berlin Heidelberg
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Bruyère, V., De Felice, C., Guaiana, G. (1994). Coding with traces. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_154
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DOI: https://doi.org/10.1007/3-540-57785-8_154
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