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Homomorphic Representations of Certain Classes of Languages

In: Advances in Algorithms, Languages, and Complexity

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  • Franz J. Brandenburg

    (Universität Passau, Lehrstuhl für Informatik)

Abstract

The use of homomorphisms for simple representations of certain classes of languages is investigated. The homomorphisms are combined to tuples which then define a homomorphic replication. This operation plays an important role in the characterization of classes of languages like BNP and MULTI-RESET. If the homomophisms of a tuple coincide on a string, then their homomorphic equality is defined. This operation is closely related to equality sets of homomorphisms and is extremely powerful. We provide purely homomorphic characterizations of the regular sets and the recursively enumerable sets, and of the classes MULTI-RESET and BNP. Starting from {$}, three homomorphisms suffice to represent every regular set and four homomorphisms suffice to represent every recursively enumerable set. For these statements we make extensive use of notions, techniques and results introduced by Professor Ron Book.

Suggested Citation

  • Franz J. Brandenburg, 1997. "Homomorphic Representations of Certain Classes of Languages," Springer Books, in: Ding-Zhu Du & Ker-I Ko (ed.), Advances in Algorithms, Languages, and Complexity, pages 93-110, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3394-4_4
    DOI: 10.1007/978-1-4613-3394-4_4
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