Asynchronous sliding block maps

Marie-Pierre Béal; Olivier Carton

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 2, page 139-156
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Béal, Marie-Pierre, and Carton, Olivier. "Asynchronous sliding block maps." RAIRO - Theoretical Informatics and Applications 34.2 (2010): 139-156. <http://eudml.org/doc/222032>.

@article{Béal2010,
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. },
author = {Béal, Marie-Pierre, Carton, Olivier},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {asynchronous sliding block map; transducer},
language = {eng},
month = {3},
number = {2},
pages = {139-156},
publisher = {EDP Sciences},
title = {Asynchronous sliding block maps},
url = {http://eudml.org/doc/222032},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Béal, Marie-Pierre
AU - Carton, Olivier
TI - Asynchronous sliding block maps
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 139
EP - 156
AB - 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.
LA - eng
KW - asynchronous sliding block map; transducer
UR - http://eudml.org/doc/222032
ER -

References

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  14. C. Frougny and J. Sakarovitch, Synchronisation déterministe des automates à délai borné. Theoret. Comput. Sci.191 (1998) 61-77.  
  15. K.A.S. Immink, P.H. Siegel and J.K. Wolf, Codes for digital recorders. IEEE Trans. Inform. Theory44 (1998) 2260-2300.  Zbl0933.94007
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