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On the size of transducers for bidirectional decoding of prefixcodes

Published online by Cambridge University Press:  23 February 2012

Laura Giambruno and
Sabrina Mantaci
Laura Giambruno
Affiliation:
Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy. lgiambr@math.unipa.it; sabrina@math.unipa.it
Sabrina Mantaci
Affiliation:
Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy. lgiambr@math.unipa.it; sabrina@math.unipa.it

Abstract

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In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci.411 (2010) 1785–1792] a bideterministic transducer is defined forthe bidirectional deciphering of words by the method introduced by Girod [IEEECommun. Lett. 3 (1999) 245–247]. Such a method is defined usingprefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and atransducer that allows both right-to-left and left-to-right decoding by this method isdefined. It is proved also that this transducer is minimal. Here we consider the number ofstates of such a transducer, related to some features of the considered prefix codeX. We find some bounds of such a number of states in relation withdifferent notions of “size” of X. In particular, we give an exact formulafor the number of states of transducers associated to maximal prefix codes. We moreoverconsider two special cases of codes: maximal uniform codes and a class of codes, that wename string-codes. We show that they represent, for maximal codes, the extreme cases withregard to the number of states in terms of different sizes. Moreover we prove that prefixcodes corresponding to isomorphic trees have transducers that are isomorphic as unlabeledgraphs.

Keywords

Variable length codesprefix codesbilateral decodingtransducers

References

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