By Stephen L. Bloom, Zoltan Ésik, Werner Kuich (auth.), Symeon Bozapalidis, George Rahonis (eds.)
This ebook constitutes the refereed complaints of the 3rd overseas convention on Algebraic Informatics, CAI 2009, held in Thessaloniki, Greece, in may perhaps 2009.
The sixteen complete papers have been conscientiously reviewed and chosen from 25 submissions. The papers disguise issues akin to algebraic semantics on graph and bushes, formal strength sequence, syntactic gadgets, algebraic photo processing, finite and limitless computations, acceptors and transducers for strings, bushes, graphs arrays, and so on. selection difficulties, algebraic characterization of logical theories, technique algebra, algebraic algorithms, algebraic coding concept, algebraic elements of cryptography.
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Extra resources for Algebraic Informatics: Third International Conference, CAI 2009, Thessaloniki, Greece, May 19-22, 2009, Proceedings
In addition there are rules whose right part is a single terminal. Notice that tile grammars may be viewed as extending CF grammars from one to two dimensions: the argument that such grammars in one dimension are essentially CF grammars allowing a local regular expression in right parts of rules is in . The derivation process of a picture starts from a S-picture. Picture derivation is a relation between partitioned pictures. Definition 15. Consider a grammar G = (Σ, N, S, R), let p, p ∈ (Σ ∪ N )h,k be pictures of identical size.
Definition 16. The picture language defined by a grammar G (written L(G)) is the set of p ∈ Σ +,+ such that ∗ S |p| , dom(p) ⇒G (p, I), where I denotes the partition of dom(p) defined by single pixels. For short we also ∗ write S ⇒G p. L(T G) denote the family of languages generated by some tile grammar. Example 1. One row and one column of b’s. The set of pictures such that there is one row and one column (both not at the border) that hold b’s, and the remainder of the picture is filled with a’s is defined by the tile grammar (we remind the reader that p stands for the set of all subpictures of size (2,2) of p): S→ Ai → # # # # # # X Ai Ai # # X Ai Ai # # # # # # # # # A1 A1 H1 A3 A3 # # # # # # | # A1 A1 H1 A3 A3 # # V1 V1 V1 V2 V2 # # A2 A2 H2 A4 A4 # # A2 A2 H2 A4 A4 # #### #XX# #### # # # # # # # , for 1 ≤ i ≤ 4 Picture Languages: From Wang Tiles to 2D Grammars X→ ##### #AXX# ##### ## # # # # B H i Hi # ## # # # | a; Hi → A → a; B → b; Vi → # # # # # # B Vi Vi # # # # # # 35 | b, for 1 ≤ i ≤ 2 | b, for 1 ≤ i ≤ 2.
31]) A regular expression on the alphabet Σ is defined recursively as follows: 1. ∅ and each a ∈ Σ are regular expressions; 2. if α and β are regular expressions, also α ∪ β, α ∩ β, αC , α are so. β, α β, α∗ , α∗ Each regular expression over Σ denotes a picture language: ∅ and a ∈ Σ denote respectively the empty language and the language formed by the unique picture of size (1, 1) with p(1, 1) = a, α∪β, α∩β , α β, α β, denote the union, intersection, row and column concatenation of languages α and β; αC , α∗ , α∗ denote the complement, and Kleene’s closures of language α.
Algebraic Informatics: Third International Conference, CAI 2009, Thessaloniki, Greece, May 19-22, 2009, Proceedings by Stephen L. Bloom, Zoltan Ésik, Werner Kuich (auth.), Symeon Bozapalidis, George Rahonis (eds.)