Showing papers by "Andrei V. Kelarev published in 2003"
Book•
01 Jan 2003
TL;DR: This work defines graph algebras and reveals their applicability to automata theory and explores assorted monoids, semigroups, rings, codes, and other algebraic structures to outline theorems and algorithms for finite state automata and grammars.
Abstract: Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. They are used to identify nontrivial connections across notions, expose conceptual properties, and mediate the application of methods from one area toward questions of the other four. After a concentrated review of the prerequisite mathematical background, Graph Algebras and Automata defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures and to outline theorems and algorithms for finite state automata and grammars.
201 citations
TL;DR: This work investigates Cayley graphs of semigroups and shows that they sometimes enjoy properties analogous to those of the Cayley graph of groups.
Abstract: We investigate Cayley graphs of semigroups and show that they sometimes enjoy properties analogous to those of the Cayley graphs of groups.
119 citations
TL;DR: This work considers automata defined by graph algebras of directed graphs, characterize all congruences on these automata, and gives a complete description of all automata of this type satisfying three properties for congruence.
16 citations
01 Jul 2003
5 citations
TL;DR: Using a (d + 1)-shortest-paths algorithm, a new more efficient algorithm is developed for the d-cycle problem with running time O(n2d-1 + n2m + n3 log n).
3 citations
TL;DR: For all finite p -groups, the Jacobson radicals of incidence rings of group automata are described and the proposed solution to the inequality of the following type is described.
Abstract: For all finite p -groups, we describe the Jacobson radicals of incidence rings of group automata.
3 citations
TL;DR: The main theorem of this paper gives a formula for the largest minimum distance of error-correcting codes considered as ideals in incidence rings defined by directed graphs.
Abstract: The main theorem of this paper gives a formula for
the largest minimum distance of error-correcting codes
considered as ideals in incidence rings defined by
directed graphs.
2 citations
Journal Article•
TL;DR: A first basic practical polynomial algorithm for finding all maximal repeated rectangular patterns in an image is included to illustrate the general approach to string processing.
Abstract: This paper begins with a brief overview of formal concepts involved in specification of images in spatial information systems. It is shown how several efficient string processing algorithms can be used for approximation, compression and analysis of images. We discuss main adjustments required for applying string algorithms in order to analyze spatial data. A first basic practical polynomial algorithm for finding all maximal repeated rectangular patterns in an image is included to illustrate our general approach.