Combinatorical and Algebraic Structures Seminar

Date:	8.11.2011
Speaker:	Tatiana Jajcayova, Rose-Hulman Institute of Technology, U.S.A.
Title:	Inverse Word Graphs
Abstract:	In the talk, we will introduce graphs (automata) that are closely related to inverse semigroups (as Cayley graphs are related to groups). Inverse semigroups can be viewed as natural generalization of groups: As every group can be represented as permutations (one-to-one transformations), inverse semigroups can be represented as partial one-to-one transformations. We will consider actions of special groups on the graph related to an inverse semi-group, which will allow us to answer some structural questions about the original semigroup. In special cases, that we will look at, automata are in general infinite, but they contain a very strong finiteness -- finite core -- in the sense that all important information about the automaton is encoded in a ``finite'' subgraph. This will alow us to answer some algorithmic questions (the Word Problem, for instance) for a given semigroup. We will also address the question of languages recognized by these automata.
Slides:	20111108.pdf

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