03040nam 22006375 450 991048358600332120251113202335.03-030-55215-210.1007/978-3-030-55215-2(CKB)4100000011435812(DE-He213)978-3-030-55215-2(MiAaPQ)EBC6348314(PPN)250220490(EXLCZ)99410000001143581220200910d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierProfinite Semigroups and Symbolic Dynamics /by Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (IX, 278 p. 67 illus., 4 illus. in color.) Lecture Notes in Mathematics,1617-9692 ;22743-030-55214-4 This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.Lecture Notes in Mathematics,1617-9692 ;2274Group theoryComputer scienceMathematicsDiscrete mathematicsDynamical systemsMachine theoryGroup Theory and GeneralizationsDiscrete Mathematics in Computer ScienceDynamical SystemsFormal Languages and Automata TheoryGroup theory.Computer scienceMathematics.Discrete mathematics.Dynamical systems.Machine theory.Group Theory and Generalizations.Discrete Mathematics in Computer Science.Dynamical Systems.Formal Languages and Automata Theory.512.2512.2Almeida Jorge1005289MiAaPQMiAaPQMiAaPQBOOK9910483586003321Profinite semigroups and symbolic dynamics2311010UNINA