On the root of languages. (English) Zbl 1022.68071
Summary: We study the problem of determining an unambiguous \(p\)-root of a language, i.e. a solution of the equation \(X^p= L\) when \(L\) is a language and the product is unambiguous. We show that every language admits at most one unambiguous root and that the problem of the existence of the unambiguous root is undecidable for the class of context free languages. We also prove that it is decidable whether a regular language admits a regular unambiguous root and that if a language is in \(P\) and admits the unambiguous root, then the root is in \(P\).
MSC:
68Q45 | Formal languages and automata |
68Q70 | Algebraic theory of languages and automata |
68Q17 | Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) |
References:
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[2] | DOI: 10.1016/0304-3975(80)90069-9 · Zbl 0415.68023 · doi:10.1016/0304-3975(80)90069-9 |
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[5] | DOI: 10.1007/3-540-08860-1_27 · doi:10.1007/3-540-08860-1_27 |
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