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Asynchronous sliding block maps

Published online by Cambridge University Press:  15 April 2002

Marie-Pierre Béal  and
Olivier Carton
Marie-Pierre Béal
Affiliation:
Institut Gaspard Monge, CNRS, Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France; ([email protected] and Url: http://www-igm.univ-mlv.fr/~beal/)
Olivier Carton
Affiliation:
Institut Gaspard Monge, CNRS, Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France; ([email protected] and Url : http://www-igm.univ-mlv.fr/~carton/)
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Abstract

We define a notion of asynchronous sliding block map that can be realized by transducers labeled in A* × B*. We show that, under some conditions, it is possible to synchronize this transducer by state splitting, in order to get a transducer which defines the same sliding block map and which is labeled in A × Bk, where k is a constant integer. In the case of a transducer with a strongly connected graph, the synchronization process can be considered as an implementation of an algorithm of Frougny and Sakarovitch for synchronization of rational relations of bounded delay. The algorithm can be applied in the case where the transducer has a constant integer transmission rate on cycles and has a strongly connected graph. It keeps the locality of the input automaton of the transducer. We show that the size of the sliding window of the synchronous local map grows linearly during the process, but that the size of the transducer is intrinsically exponential. In the case of non strongly connected graphs, the algorithm of Frougny and Sakarovitch does not keep the locality of the input automaton of the transducer. We give another algorithm to solve this case without losing the good dynamic properties that guaranty the state splitting process.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 2 , March 2000 , pp. 139 - 156
Copyright
© EDP Sciences, 2000

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References

R.L. Adler, D. Coppersmith and M. Hassner, Algorithms for sliding block codes. IEEE Trans. Inform. Theory IT-29 (1983) 5-22.
A. Aho, R. Sethi and J. Ullman, Compilers. Addison-Wesley (1986).
Ashley, J.J., Factors and extensions of full shifts I. IEEE Trans. Inform. Theory 34 (1988) 389-399. CrossRef
Ashley, J.J., A linear bound for sliding-block decoder window size, II. IEEE Trans. Inform. Theory 42 (1996) 1913-1924. CrossRef
M.-P. Béal, Codage Symbolique. Masson (1993).
M.-P. Béal and O. Carton, Asynchronous sliding block maps, in Proc. of DLT'99 (2000) (to appear).
M.-P. Béal and D. Perrin, Symbolic dynamics and finite automata, in Handbook of Formal Languages, edited by G. Rosenberg and A. Salomaa, Vol. 2. Springer (1997), Chap. 10.
C. Berge, Graphes. Gauthier-Villar (1983).
J. Berstel, Transductions and Context-Free Languages. B.G. Teubner (1979).
J. Berstel and D. Perrin, Theory of Codes. Academic Press (1984).
S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press, New York (1972).
Elgot, C.C. and Mezei, J.E., On relations defined by generalized finite automata. IBM J. Res. Develop. 9 (1965) 47-68. CrossRef
Frougny, C. and Sakarovitch, J., Synchronized relations of finite words. Theoret. Comput. Sci. 108 (1993) 45-82. CrossRef
Frougny, C. and Sakarovitch, J., Synchronisation déterministe des automates à délai borné. Theoret. Comput. Sci. 191 (1998) 61-77. CrossRef
Immink, K.A.S., Siegel, P.H. and Wolf, J.K., Codes for digital recorders. IEEE Trans. Inform. Theory 44 (1998) 2260-2300. CrossRef
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press (1995).
Marcus, B., Factors and extensions of full shifts. Monatsh. Math. 88 (1979) 239-247. CrossRef
B. Marcus, R. Roth and P. Siegel, Handbook of Coding Theory, Vol. 2. Elsevier (1998), chap. Constrained Systems and Coding for Recording Channels.