Prefix-Free Subsets of Regular Languages and Descriptional Complexity

Jirásek, Jozef; Šebej, Juraj

doi:10.1007/978-3-319-19225-3_11

Cited by 2 publications

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“…In terms of information theory, quality could be the average word length, or the efficiency of encoding information, for instance. In terms of automaton theory, investigate the state complexity of the regular maximal languages in terms of the state complexity of the initial language, for various cases of t. A study of this type for prefix codes can be found in [9].…”

Section: Discussionmentioning

confidence: 99%

“…Example 30. In [9] the authors consider computing a maximal prefix code that is a subset of a given regular language L. We can replace prefix code with t-independent language, for any suitable input-decreasing transducer t, and approach this generalized problem by first computing X = L − t −1 (L), which is always t-independent, and then use the iterated max-min operator to embed X into a maximal t-independent language relative to M = L. The work in [9] provides further results on maximal prefix codes that can possibly be extended to certain t-independences-see also the last section for further comments.…”

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Embedding rationally independent languages into maximal ones

Konstantinidis¹,

Mastnak²

2015

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We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language L, find a maximal independent language containing L. We consider the case where the code-related property is defined via a rational binary relation that is decreasing with respect to any fixed total order on the set of words. Our method works by iterating a max-min operator that has been used before for the embedding problem for properties defined by length-increasing-and-transitive binary relations. By going to order-decreasing rational relations, represented by inputdecreasing transducers, we are able to include many known properties from both the noiseless and noisy domains of coding theory, as well as any combination of such properties. Moreover, in many cases the desired maximal embedding is effectively computable.

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confidence: 99%

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confidence: 99%