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International Conference on Descriptional Complexity of Formal Systems

DCFS 2017: Descriptional Complexity of Formal Systems pp 33–44Cite as

Descriptional Complexity and Operations – Two Non-classical Cases

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10316))

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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Authors and Affiliations

  1. Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39016, Magdeburg, Germany

    Jürgen Dassow

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  1. Jürgen Dassow
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Correspondence to Jürgen Dassow .

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Editors and Affiliations

  1. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  2. University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada

    Cezar Câmpeanu

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Dassow, J. (2017). Descriptional Complexity and Operations – Two Non-classical Cases. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-60252-3_3

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-60252-3

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