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Complexity of proper prefix-convex regular languages

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1-s2.0-S0003267018313047-main.pdf (614.75 KB)

Date

2019-10-01

Authors

Brzozowski, Janusz
Sinnamon, Corwin

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

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, which were studied elsewhere. Here we concentrate on prefix-convex languages that do not belong to any one of these classes; we call such languages proper. We exhibit most complex proper prefix-convex languages, which meet the bounds for the size of the syntactic semigroup, reversal, complexity of atoms, star, product, and boolean operations.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.07.015. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

atom, most complex, prefix-convex, proper, quotient complexity, regular language, state complexity, syntactic semigroup

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Citation

URI

https://doi.org/10.1016/j.tcs.2018.07.015
 http://hdl.handle.net/10012/15697

Collections

Waterloo Research
Computer Science