Syntactic complexity of bifix-free regular languages

Szykuła, Marek; Wittnebel, John

doi:10.1016/j.tcs.2018.12.025

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2019

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“…It is also an interesting question to determine the alphabet size needed to reach the maximum possible syntactic complexity: for the whole class of regular languages, an alphabet of ternary size suffices, but e.g. for factor-closed languages an alphabet of size 6 is needed [4], while for bifix-free languages (n − 2) n−3 + (n − 3)2 n−3 − 1 generators are needed if n ≥ 6 [13].…”

Section: Introductionmentioning

confidence: 99%

The Syntactic Complexity of Semi-flower Languages

Gelle

Iván

2019

Descriptional Complexity of Formal Systems

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Semi-flower languages are those of the form L * for some finite maximal prefix code L, or equivalently, those recognizable by a so-called semi-flower automaton, in which all the cycles have a common state q0, which happens to be the initial state and the only accepting state. We show that the syntactic complexity of these languages is exactly n n − n! + n (where n stands for the state complexity as usual) and that this bound is reachable with an alphabet of size n.

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Section: Introductionmentioning

confidence: 99%