Complexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languages
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Date
2017
Authors
Brzozowski, Janusz
Sinnamon, Corwin
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Informatics: University of Szeged
Abstract
A language L over an alphabet E is prefix-convex if, for any words x, y, z is an element of Sigma*, 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 semi group, and the quotient complexity of atoms. For binary operations we use arguments with different alphabets when appropriate; this leads to higher tight upper bounds than those obtained with equal alphabets. We exhibit right-ideal, prefix-closed, and prefix-free languages that meet the complexity bounds for all the measures listed above.
Description
Keywords
atoms, complexity of operations, prefix-closed, prefix-convex, prefix-free, quotient complexity, regular languages, right ideals, state complexity, syntactic semigroup, unrestricted alphabets