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 party of his retirement after greater than 35 years of training. the subjects lined are: weighted automata over phrases and timber, tree transducers, quantum automata, graphs, images and kinds of semigroups.

Since 1982 -- on the Aristotle college of Thessaloniki -- Symeon's major pursuits were heavily attached with the algebraic foundations in laptop technology. particularly, he contributed to the advance of the speculation of tree languages and sequence, the axiomatization of graphs, photograph idea, and fuzzy languages.

The quantity, which specializes in the learn pursuits of Symeon, includes 15 completely refereed invited papers, written via his colleagues, neighbors, and scholars. many of the papers have been provided 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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**Extra resources for Algebraic Foundations in Computer Science: Essays Dedicated to Symeon Bozapalidis on the Occasion of His Retirement**

**Sample text**

Dl , written in base-k notation. In other words, num(w) = i∈[l] di k −i . Thus, a pair (w, w ) of strings over Σ can be encoded as a point in U , namely (num(w), num(w )). Note that num is injective, because 0 ∈ / Σ. Hence, (num(w), num(w )) lies on the diagonal if and only if w = w . We will also need to encode the lengths of w and w . This is done by representing (w, w ) as the rectangle rec[w, w ] = [p : p ], where p = (num(w), num(w )) and p = (num(w) + k −|w| , num(w ) + k −|w | ). The following lemma is the reason why we have to assume preﬁx-freeness.

Regulated Rewriting in Formal Language Theory. EATCS Monographs in Theoretical Computer Science. Springer, Berlin (1989) 5. : Language theoretic and algorithmic properties of d-dimensional collages and patterns in a grid. Journal of Computer and System Sciences 53, 33–60 (1996) 6. : Tree-based generation of languages of fractals. Report 2/99, Univ. Bremen (1999); revised version appeared in Theoretical Computer Science 7. : Tree-based picture generation. Theoretical Computer Science 246, 1–51 (2000) 8.

Due to the statement above, each sequence Û forms only a ﬁnite number of preﬁxes of π. Let k be the length of the longest preﬁx of π which a sequence Û can form. Consequently, no value W ∈ im( M ) contains a word from {1, 2}∗ that is a preﬁx of π of length greater than k. Let u ∈ {1, 2}∗ − be a preﬁx of π of length at least k + 1 and let t ∈ TΣ be a tree with ← u ∈ dom(t). Then u ∈ S(t) but u ∈ / M (t). Hence, M = S. 2. We ﬁx a linear order < on K such that {1} < {2}. Now we deﬁne the tree series S for all t ∈ TΣ by ⎧ n n ⎪ ⎨{1 2 } S (t) = 1n+1 2n ⎪ ⎩ ∅ if t ∈ T{a(0) ,b(1) } ∧ ∃n ∈ IN0 : |dom(t)| = 2n, if t ∈ T{a(0) ,b(1) } ∧ ∃n ∈ IN0 : |dom(t)| = 2n + 1, otherwise.

### 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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