On shuffle ideals

Héam, Pierre-Cyrille

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 36 (2002) no. 4, pp. 359-384

A shuffle ideal is a language which is a finite union of languages of the form $A^{*}{a}_1{A}^{*}\cdots A^{*}{a}_k{A}^{*}$ where $A$ is a finite alphabet and the $a_i$’s are letters. We show how to represent shuffle ideals by special automata and how to compute these representations. We also give a temporal logic characterization of shuffle ideals and we study its expressive power over infinite words. We characterize the complexity of deciding whether a language is a shuffle ideal and we give a new quadratic algorithm for this problem. Finally we also present a characterization by subwords of the minimal automaton of a shuffle ideal and study the complexity of basic operations on shuffle ideals.

Classification: 68Q45, 68Q70

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