Get Algebraic Foundations in Computer Science: Essays Dedicated PDF

By Frank Drewes (auth.), Werner Kuich, George Rahonis (eds.)

ISBN-10: 3642248969

ISBN-13: 9783642248962

This Festschrift quantity is released in honor of Symeon Bozapalidis at the social gathering of his retirement after greater than 35 years of training. the themes lined are: weighted automata over phrases and bushes, tree transducers, quantum automata, graphs, photographs and different types of semigroups.

Since 1982 -- on the Aristotle collage of Thessaloniki -- Symeon's major pursuits were heavily hooked up with the algebraic foundations in computing device technological know-how. specifically, he contributed to the improvement of the idea of tree languages and sequence, the axiomatization of graphs, photo thought, and fuzzy languages.

The quantity, which makes a speciality of the examine pursuits of Symeon, includes 15 completely refereed invited papers, written through his colleagues, buddies, and scholars. many of the papers have been provided on the Workshop on Algebraic Foundations in computing device technological know-how, held in Thessaloniki, Greece, in the course of November 7--8, 2011.

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Let w, w ∈ Σ ∗ be such that neither is a prefix of the other. If num(w) < num(w ), then num(w) + k −|w| ≤ num(w ). Proof. Let w = d1 · · · dl and w = d1 · · · dm . Since w is not a prefix of w , there is a j ∈ [min(l, m)] such that d1 = d1 , . . , dj−1 = dj−1 , and dj < dj . Hence, num(w) + k −|w| = i∈[l] di k −i + k −l = i∈[j−1] di k −i + (dj + 1)k −j ≤ i∈[j] di k −i ≤ num(w ). Now, consider the collage grammar GPCP = ({S}, {β}, r1 , . . , rk , r1 , . . 8 By Lemma 19, this collage grammar is a grid collage grammar, where the grid is 1 1 determined by num(π11 ), num(π11 ) + k −|π1 | , .

If D is left-distributive, then S is recognizable iff S = [[ϕ]] for a ∀-restricted and ∧-restricted wMSO sentence ϕ. 3. If D is a cctv-semiring, then S is recognizable iff S = [[ϕ]] for a ∀-restricted and commutatively ∧-restricted wMSO sentence ϕ. Obviously, we need D to be regular. Otherwise, there is at least one d ∈ D without a wta recognizing d, hence, the semantics of the ∀-restricted and strongly ∧-restricted sentence d is not recognizable. 5, we will give two examples taken from [43] showing that it is not possible to dispose of any constraint in the above theorem.

I − 1) ∈ B. i ∈ B, the tree domain B is prefix-closed. A tree over a set M (of labels) is a mapping t : B → M Weighted Tree Automata and Weighted Logics over Valuation Monoids 33 such that dom(t) = B is a tree domain. The elements of dom(t) are called positions of t and t(u) is called label of t at u ∈ dom(t). The set of all labels of t is defined by the image of t, thus by im(t) = {t(u) | u ∈ dom(t)}. We denote the set of all trees over M by TM . A tree language is a subset of TM . i ∈ dom(t)} | = k whenever t(u) ∈ Σ (k) .

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Algebraic Foundations in Computer Science: Essays Dedicated to Symeon Bozapalidis on the Occasion of His Retirement by Frank Drewes (auth.), Werner Kuich, George Rahonis (eds.)

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