# Descriptional Complexity and Operations – Two Non-classical Cases

Abstract : For a language family $\mathcal{L}$, a syntactic complexity measure K defined on languages of $\mathcal{L}$, a number $n\ge 1$, and an n-ary operation $\circ$ under which $\mathcal{L}$ is closed, we define $g_{\circ }^K(m_1,m_2,\dots ,m_n)$ as the set of all integers r such that there are n languages $L_i$, $1\le i\le n$, with $K(L_i)=m_i \text { for } 1\le i\le n \text { and } K(\circ (L_1,L_2,\dots ,L_n))=r.$In this paper we study these sets for the operation union, catenation, star, complement, set-subtraction, and intersection and the measure number of accepting states (defined for regular languages) as well as for reversal, union, catenation, and star and the measures number of nonterminals, productions, and symbols (defined for context-free languages).Moreover, we discuss the change of these sets if one restricts to finite languages, unary languages, and finite unary languages.
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Submitted on : Wednesday, December 6, 2017 - 11:43:59 AM
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### Citation

Jürgen Dassow. Descriptional Complexity and Operations – Two Non-classical Cases. 19th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2017, Milano, Italy. pp.33-44, ⟨10.1007/978-3-319-60252-3_3⟩. ⟨hal-01657004⟩

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