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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 15, Issue 1 (Jan 2007)


Formal Languages - Concatenation and Closure

Michał Trybulec
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-007-0002-y

Formal Languages - Concatenation and Closure

Formal languages are introduced as subsets of the set of all 0-based finite sequences over a given set (the alphabet). Concatenation, the n-th power and closure are defined and their properties are shown. Finally, it is shown that the closure of the alphabet (understood here as the language of words of length 1) equals to the set of all words over that alphabet, and that the alphabet is the minimal set with this property. Notation and terminology were taken from [5] and [13].

MML identifier: FLANG 1, version: 7.8.04 4.81.962

  • [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [4] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [5] John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley Publishing Company, 1979.Google Scholar

  • [6] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Google Scholar

  • [7] Karol Pąak. The Catalan numbers. Part II. Formalized Mathematics, 14(4):153-159, 2006.Google Scholar

  • [8] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.Google Scholar

  • [9] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Google Scholar

  • [10] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.Google Scholar

  • [11] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [12] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.Google Scholar

  • [13] William M. Waite and Gerhard Goos. Compiler Construction. Springer-Verlag New York Inc., 1984.Google Scholar

  • [14] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

About the article

Published Online: 2008-06-13

Published in Print: 2007-01-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0002-y.

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