Formal and Natural Computing: Essays Dedicated to Grzegorz - download pdf or read online

By Jean Berstel, Luc Boasson (auth.), Wilfried Brauer, Hartmut Ehrig, Juhani Karhumäki, Arto Salomaa (eds.)

ISBN-10: 354043190X

ISBN-13: 9783540431909

This publication provides state-of-the-art examine in theoretical machine technology and similar ?elds. specifically, the next parts are mentioned: automata concept, formal languages and combinatorics of phrases, graph changes, Petri nets, concurrency, in addition to average and molecular computing. The articles are written via prime researchers in those components. The writers have been initially invited to give a contribution to this ebook yet then the traditional refereeing process used to be utilized in addition. the entire articles take care of a few factor that has been below full of life learn in the course of contemporary years. nonetheless, the subjects diversity from very classical ones to matters raised simply or 3 years in the past. either survey articles and papers attacking speci?c study difficulties are integrated. The booklet highlights a few key problems with theoretical laptop technological know-how, as they appear to us now first and foremost of the hot millennium. Being a accomplished evaluate of a few of the main lively present study in theoretical laptop technological know-how, it's going to be of de?nite curiosity for all researchers within the parts lined. the themes variety from simple decidability and the thought of data to graph grammars and graph ameliorations, and from timber and strains to aqueous algorithms, DNA encoding and self-assembly. distinct e?ort has been given to lucid presentation. as a result, the booklet might be of curiosity additionally for complicated students.

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Additional info for Formal and Natural Computing: Essays Dedicated to Grzegorz Rozenberg

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It follows that α −→ t. This proves the inclusion. Consider now the converse inclusion L(G, α) ⊂ L(G , U ) α∈U This means that, for each word w ∈ L(G, α), there exists a set U containing α such that w ∈ L(G , U ). We shall in fact prove the following, slightly more general property. Let m ∈ ∗ (V ∪ A)∗ . If α −→ m, then for every set M containing m, there exists a set U ∗ containing α such that U −→ m. Assume indeed that α −→ m. If = 1, choose any “big word” M containing m and let U = {γ | M ∈ Rγ }.

Then agyd¯ a ∈ [X]. Consequently agzd¯ a ∈ [X], showing that rqs ∈ RX,a , and therefore p ≈ q. This shows that to each equivalence class of ≡L intersecting D∗ corresponds one equivalence class of RX,a . Since there are finitely many of the former, there are finitely may of the second, and RX,a is regular. Conversely, assume now that L is balanced. Then it is of course well-formed. Consider a codeterministic balanced grammar G generating L. Let u ∈ D∗ be a Dyck word that is a factor of some word in L, and set u = v1 · · · vn , with v1 , .

The grammar X0 → Y a¯ a X → aY a ¯ | aa Y → aX¯ aa ¯aa¯ a | aY a ¯a ¯a ¯aX¯ a generates a balanced language. It was used by Knuth ([6]) to demonstrate how his algorithm for the effective construction of a balanced grammar works. 2 Decision Problems In this section, we state two decidability results. There are other decision problems that will be considered later. The following result was proved in [1]. It will be used later. 10. Given a context-free language L over an alphabet A ∪ A, ¯ decidable whether L is a subset of the set DA of Dyck primes over A ∪ A.

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Formal and Natural Computing: Essays Dedicated to Grzegorz Rozenberg by Jean Berstel, Luc Boasson (auth.), Wilfried Brauer, Hartmut Ehrig, Juhani Karhumäki, Arto Salomaa (eds.)

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