Semigroups and Combinatorial ApplicationsThe purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures. |
Contents
Elementary Definitions and Examples | 1 |
Greens Relations | 19 |
Simple Semigroups ReesSuschkewitsch Theorem | 53 |
Copyright | |
14 other sections not shown
Common terms and phrases
0-simple A*-automaton A₁ algebraic language algorithm alphabet assume bijection biprefix C₁ C₂ called Chapter closure complete prefix code completely 0-simple completes the proof computable congruence contains Corollary cyclic D-class d₁ decomposition defined definition denote elements equivalent example exists f(So f₁ finite monoids finite number follows free monoid free semigroup function G₁ G₂ grammar Green's relations group G H₁ Hence homomorphism idempotent implies induction integer isomorphic L₁ L₂ left factor Lemma letter M. P. Schützenberger m₁ m₂ mapping matrix maximal subgroup minimal ideal modulo obtain P₁ pairs partial recursive power-series prefix code Proposition pseudovariety quotient R₁ rational languages Rees matrix semigroup relation resp satisfying Section semiring shows simple semigroup submonoid subsemigroup subset surjective syntactic monoid t-monoid t₁ t₂ Theorem transformation semigroup transition monoid u₁ unique v₁ w₁ w₂ x₁