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On the combinatorial alphabets of a language

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Daniel-Claudian VoinescuAuthors Info & Claims

Journal of Automata, Languages and Combinatorics, Volume 7, Issue 3

Pages 377 - 394

Published: 01 January 2002 Publication History

Abstract

The combinatorial degree (or dimension) of a language L over a finite alphabet Σ is the positive integer d(L) = min{card(A) | A ⊂ Σ*, L ⊂ A*}. A subset A of Σ* for which L ⊂ A* and card (A) = d(L) will be called a combinatorial alphabet of the language L. The set of all the combinatorial alphabets of L will be denoted by CA(L). In this paper we shall establish the main properties and the structure of CA(L) and also we shall prove that for every language L there exists a finite part L_f - which will be called, by analogy with the famous notion of a test-set, a finite combinatorial test-set - such that CA(L) = CA(L_f). We shall prove also that each language has a finite subset which is simultaneously a test-set and a combinatorial test-set, we shall highlight some relations between test-sets and combinatorial test-sets and we shall give some interesting examples.

References

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Index Terms

On the combinatorial alphabets of a language
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Algebraic language theory

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cover image Journal of Automata, Languages and Combinatorics

Journal of Automata, Languages and Combinatorics Volume 7, Issue 3

January 2002

115 pages

ISSN:1430-189X

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Otto-von-Guericke-Universitat

Germany

Publication History

Published: 01 January 2002

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Abstract

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Recommendations

(Prefix) reversal distance for (signed) strings with few blocks or small alphabets

Reversals and Transpositions Over Finite Alphabets

Cyclically repetition-free words on small alphabets

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