Jürgen Albert, German Tischler (auth.), Symeon Bozapalidis,'s Algebraic Informatics: Second International Conference, CAI PDF

By Jürgen Albert, German Tischler (auth.), Symeon Bozapalidis, George Rahonis (eds.)

This booklet constitutes the refereed court cases of the second one overseas convention on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in could 2007.

The 10 revised complete papers provided including 9 invited papers have been conscientiously reviewed and chosen from 29 submissions. The papers hide themes corresponding to algebraic semantics on graphs and bushes, formal strength sequence, syntactic gadgets, algebraic photograph processing, endless computation, acceptors and transducers for strings, timber, graphs, arrays, etc., and determination problems.

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A set X of words over an alphabet A is -balanced if, for each x, y in X of equal length, |x|a − |y|a ≤ for all letters a. Here |x|a denotes the number of occurrences of a in x. A word is -balanced if the set of its factors is balanced. Binary balanced words are precisely 1-balanced words. A word w is strongly balanced if w is primitive and w2 is balanced. A word w such that w2 is balanced, without being necessarily primitive is called cyclically balanced in [42]. Thus a word is cyclically balanced if it is a power of some strongly balanced word.

For this reason, we choose a least fixed-point semantics for delegation networks (Definition 5). The structure of this paper is thus as follows. In the next section, the basic notions regarding tree-based generators are recalled. In Section 3, the tree-based versions of some well-known grammatical devices are discussed. Section 4 introduces delegation networks, which are illustrated by means of an example in Section 5. Section 6 concludes the paper. 2 Tree-Based Generators Before recalling the notion of tree-based generators, let us summarize some standard notions and notation.

The (right) degree degw (x) of a finite word x in w is the number of letters a such that xa is a factor of w: degw (x) = Card{a ∈ A | xa ∈ F (w)} Similarly, the left degree of w is the number of a ∈ A with ax ∈ F (w). Clearly, degw (x) ≥ 1 for each factor x of w. Also, degw (xy) ≤ degw (y) for all x, y. Clearly cw (n + 1) = deg(x) . x∈Fn (w) A factor x is right special (left special) if its degree (left degree) is strictly greater than 1. Any suffix of a right special factor is again right special.

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