Download Algebraic Foundations in Computer Science: Essays Dedicated by Frank Drewes (auth.), Werner Kuich, George Rahonis (eds.) PDF

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

This Festschrift quantity is released in honor of Symeon Bozapalidis at the get together of his retirement after greater than 35 years of training. the subjects lined are: weighted automata over phrases and bushes, tree transducers, quantum automata, graphs, images and kinds of semigroups.

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

The quantity, which specializes in the examine pursuits of Symeon, comprises 15 completely refereed invited papers, written by way of his colleagues, pals, and scholars. many of the papers have been offered on the Workshop on Algebraic Foundations in laptop technological know-how, held in Thessaloniki, Greece, in the course of November 7--8, 2011.

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Now, to derive a contradiction, assume that the (framed) right-hand side K is disconnected. Then there is a part P ∈ K that cannot be reached from any boundary part P ∈ K, because each of the boundary parts can be reached from any other boundary part. It follows that, in C, the image of P cannot be reached from the image of P either, contradicting the assumption that C is connected. Thus, K is connected. “⇐” By the induction hypothesis, C is connected. Thus, the image of every boundary part of K in C can be reached from every part in C \ {N }.

We call D left-multiplicative if d Val(t) = Val(t ) for all d ∈ D, t, t ∈ TD with dom(t) = dom(t ), t (ε) = d t(ε), and t (u) = t(u) for every u ∈ dom(t) \ {ε}. Furthermore, D is left-Val-distributive if d Val(t) = Val(t ) for all d ∈ D, t, t ∈ TD with dom(t) = dom(t ) and t (u) = d t(u) for every u ∈ dom(t). It is easy to see that each left-multiplicative or left-Val-distributive ptv-monoid is regular. Now, a ptv-monoid D is called left-distributive if it is left-multiplicative or left-Val-distributive and, moreover, left- -distributive.

In addition, it is conditionally commutative but neither associative nor right- -distributive and thus no cctv-semiring. Let ϕ = ∃x( a∈Σ (0) labela (x))∧2, a ∀-restricted and commutatively ∧-restricted wMSO sentence. Then [[∃x( labela (x)) ∧ 2]](t) = div a∈Σ (0) [[labela (x))]]{x} (t[x → u]), [[2]](t) u∈dom(t) a∈Σ (0) = 2 “number of leaves of t” for all t ∈ TΣ . Let M be any wta over (Q+ 0 , +, Wroot , div, 0, 1). Since the set of weights of M is finite, there is a rational number q = 2−n > 0 smaller than all weights from im(μ) \ {0}.

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