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On the size of transducers for bidirectional decoding of prefix codes. (English) Zbl 1278.94038

Summary: In a previous paper [the authors, Theor. Comput. Sci. 411, No. 16–18, 1785–1792 (2010; Zbl 1194.94177)], a bideterministic transducer was defined for the bidirectional deciphering of words by the method introduced by B. Girod [“Bidirectionally decodable streams of prefix code-words”, IEEE Commun. Lett. 3, No. 8, 245–247 (1999; doi:10.1109/4234.781009)]. Such a method is defined using prefix codes. Moreover a coding method, inspired by Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code \(X\). We find some bounds of such a number of states in relation with different notions of “size” of \(X\). In particular, we give an exact formula for the number of states of transducers associated to maximal prefix codes. We moreover consider two special cases of codes: maximal uniform codes and a class of codes that we name string-codes. We show that they represent, for maximal codes, the extreme cases with regard to the number of states in terms of different sizes. Moreover we prove that prefix codes corresponding to isomorphic trees have transducers that are isomorphic as unlabeled graphs.

MSC:

94A45 Prefix, length-variable, comma-free codes
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
68Q45 Formal languages and automata
94B35 Decoding

Citations:

Zbl 1194.94177
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References:

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[5] L. Giambruno and S. Mantaci, Transducers for the bidirectional decoding of prefix codes, Theoret. Comput. Sci.411 (2010) 1785-1792. Zbl1194.94177 · Zbl 1194.94177 · doi:10.1016/j.tcs.2010.01.033
[6] B. Girod, Bidirectionally decodable streams of prefix code words. IEEE Commun. Lett.3 (1999) 245-247.
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[8] D. Salomon, Variable-Length Codes for Data Compression. Springer-Verlag (2007). · Zbl 1194.94176
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