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

This Festschrift quantity is released in honor of Symeon Bozapalidis at the celebration of his retirement after greater than 35 years of educating. 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 attached with the algebraic foundations in laptop technological know-how. particularly, he contributed to the advance of the speculation of tree languages and sequence, the axiomatization of graphs, photograph concept, and fuzzy languages.

The quantity, which makes a speciality of the learn pursuits of Symeon, includes 15 completely refereed invited papers, written by way of his colleagues, acquaintances, and scholars. lots of the papers have been awarded on the Workshop on Algebraic Foundations in laptop technology, held in Thessaloniki, Greece, in the course of November 7--8, 2011.

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In the same way, but dropping the requirement of determinism, languages of fractals can be generated and studied. Devices of these kinds have been studied in [5,6,7,8] in the collage grammar setting and in [3] in the algebraic setting of picture-refinement grammars. Selected Decision Problems for Square-Refinement Collage Grammars 27 In view of the undecidability results of Sect. 4, it may be of interest to mention that connectedness of the fractals generated by grid IFS was shown to be a decidable problem in [5] (see also [8, Sect.

Weights appearing in a run are collected and then multiplied following their order in K. Let < be a strict linear order on the underlying set of a tv-monoid K. Then we obtain a linear order ≺wo (the weight ordering) on dom(t) for t ∈ TK by requiring t(u) < t(v) ⇒ u ≺wo v for all u, v ∈ dom(t); note that ≺wo may not be unique because a weight d can appear at several positions. But this does not effect the valuation function. We denote the corresponding enumeration by WO< . Next we show that the classes of recognizable tree series for two distinct enumerations may be different.

Proof. For linear grid collage grammars, this is immediate from Lemma 21, because the reduction constructs a linear grammar. Alternatively, we may consider GPCP = ({S}, {β}, r, r , S), where r = (S ::={(S, rec[πi1 , πi2 ]) | i ∈ [k]}), and r = (S ::={rec[πi1 , πi2 ] | i ∈ [k]}). Clearly, L(GPCP ) = L(GPCP ), which proves the assertion for grammars with two rules. 6 Concluding Remarks We have defined square-refinement collage grammars and surveyed decidability and complexity results regarding these grammars or their special cases, namely (partial-) array collage grammars, which are closely related to Bozapalidis’ picture-refinement grammars, and grid collage grammars.

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