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2002•International Journal of Foundations of Computer ScienceRequires access

SHUFFLE DECOMPOSITIONS OF REGULAR LANGUAGES

Cezar Câmpeanu, Kai Salomaa, Sándor Vágvölgyi

Open publisher page 8 citations

Abstract

We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

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What this paper is about

We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

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Available abstract

We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

Key concepts: Undecidable problem, Closure (psychology), Regular language, Equivalence (formal languages), Quotient, Decomposition, Mathematics, Context-free language

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