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By Srečko Brlek, Christophe Reutenauer

This publication constitutes the complaints of the twentieth foreign convention on advancements in Language conception, DLT 2016, held in Montreal, quality control, Canada, in July 2016.

The 32 complete papers and four abstracts of invited papers offered have been rigorously reviewed and chosen from forty eight submissions. This quantity provides present advancements in formal languages and automata, particularly from the subsequent issues and parts: combinatorial and algebraic houses of phrases and languages; grammars, acceptors and transducers for strings, bushes, graphs, arrays; algebraic theories for automata and languages; codes; effective textual content algorithms; symbolic dynamics; choice difficulties; relationships to complexity thought and good judgment; photo description and research; polyominoes and bidimentional styles; cryptography; concurrency; mobile automata; bio-inspried computing; quantum computing.

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Extra resources for Developments in Language Theory: 20th International Conference, DLT 2016, Montréal, Canada, July 25-28, 2016, Proceedings

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A subset L of A is linear if it has the form ∪i∈I (ai,1 · · · ai,ki ) where the ai and ai,j are elements L = a1 · · · ak of A and I is a finite set. It is semi-linear if it is a finite union of linear sets. The class of -rational languages of A is the smallest containing the empty set, {ε}, {a} for all a ∈ A, and closed under finite union, parallel product , and finite parallel iteration . The notions of rational, -rational, linear and semi-linear languages, which are defined over free algebras, also naturally apply to non-free algebras.

However, the class of Cayley automatic groups is considerably wider than the class of automatic groups. For example, all finitely generated nilpotent groups of nilpotency class at most two and all fundamental groups of three–dimensional manifolds are Cayley automatic [10]. The Baumslag–Solitar groups are Cayley automatic [1]. Cayley automatic groups retain the key algorithmic properties which hold for automatic groups: the word problem for Cayley automatic groups is decidable in quadratic time, the conjugacy problem for Cayley biautomatic groups is decidable, and the first order theory for Cayley graphs of Cayley automatic groups is decidable.

The following proposition shows asymptotic behavior of Eμ∗n [ S ]. Proposition 13. Let G, S and α be as above. For a symmetric simple random 1+α walk on Γ (G Z, S), Eμ∗n [ S ] n 2 . Proof. For the proof see [8, Lemma 3]. Cayley Automatic Groups and Num. Characteristics of Turing Transducers 35 Theorem 14. For every α < 1 there exists a Turing transducer T ∈ T for nβ for some β such that α < β < 1 and the growth function bn is which n exponential. Proof. Let us consider the sequence of wreath products Gm , m = 1, .

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