2017
DOI: 10.14232/actacyb.23.1.2017.3
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Complexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languages

Abstract: A language L over an alphabet Σ is prefix-convex if, for any words x, y, z ∈ Σ * , whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages as special cases. We examine complexity properties of these special prefix-convex languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal, the size of the syntactic semigroup, and the quotient complexity of atoms. For binary o… Show more

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Cited by 9 publications
(19 citation statements)
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“…The authors of [9] proved this result with t = (1 ′ , 2 ′ ), but we prove a slightly more general statement.…”
Section: Examplesmentioning
confidence: 55%
See 4 more Smart Citations
“…The authors of [9] proved this result with t = (1 ′ , 2 ′ ), but we prove a slightly more general statement.…”
Section: Examplesmentioning
confidence: 55%
“…, n − 1}. The inductive proof given by the authors of [9] has a different structure from the type of argument captured by Theorem 1. To reach a state (q ′ , S), in Theorem 1 we start from some state (q ′ , B) and apply a word that fixes the first component q ′ .…”
Section: Examplesmentioning
confidence: 99%
See 3 more Smart Citations