Finiteness and Regularity in Semigroups and Formal Languages

Luca, Aldo De; Varricchio, Stefano

ISBN 10: 3642641504 / ISBN 13: 9783642641503

Editore: Springer, 2011

Codice articolo 18724341-n

Riassunto:

This is a rigorous and self-contained monograph on a central topic in theoretical computer science. For the first time in book form, original results from the last ten years are presented, some previously unpublished, using combinatorial and algebraic methods. These are mainly based on combinatorics on words and especially on the theory of "unavoidable regularities." Researchers will find important new results on semigroups and formal languages, as well as various applications for these methods.

Contenuti: 1. Combinatorics on Words.- 1.1 Preliminaries.- 1.2 Infinite words.- 1.3 Metric and topology.- 1.4 Periodicity and conjugacy.- 1.5 Lyndon words.- 1.6 Factorial languages and subword complexity.- 2. Unavoidable Regularities.- 2.1 Ramsey’s theorem.- 2.2 Van der Waerden’s theorem.- 2.3 Uniformly recurrent words.- 2.4 Shirshov’s theorem.- 2.5 Bounded languages.- 2.6 Power-free words.- 2.7 Bi-ideal sequences.- 2.7.1 Canonical factorizations.- 2.7.2 Bi-ideal sequences and recurrence.- 2.7.3 Some extensions of the Shirshov theorem.- 3. Finiteness Conditions for Semigroups.- 3.1 Preliminaries on semigroups.- 3.2 Finitely generated semigroups.- 3.3 The Burnside problem.- 3.4 Permutation property.- 3.4.1 The weak permutability.- 3.4.2 The ?-permutability.- 3.5 Partial commutations.- 3.6 Chain conditions.- 3.6.1 The J-depth decomposition theorem.- 3.6.2 Minimal conditions on principal right ideals.- 3.6.3 Minimal conditions on principal bi-ideals.- 3.6.4 The McNaughton-Zalcstein and Straubing theorems.- 3.7 Iteration property.- 3.7.1 w-iteration property.- 3.7.2 Strong periodicity.- 3.8 Permutation and iteration property.- 3.9 Repetitivity.- 3.9.1 Repetitive morphisms and semigroups.- 3.9.2 Strongly repetitive morphisms.- 3.9.3 Uniformly repetitive semigroups.- 4. Finitely Recognizable Semigroups.- 4.1 The Myhill-Nerode theorem.- 4.2 Finitely recognizable semigroups.- 4.3 The factor semigroup.- 4.4 Rewriting systems.- 4.5 The word problem.- 4.6 On a conjecture of Brzozowski.- 4.6.1 Problems and results.- 4.7 On a conjecture of Brown.- 5. Regularity Conditions.- 5.1 Uniform conditions.- 5.2 Pumping properties.- 5.3 Permutative property.- 6. Well Quasi-orders and Regularity.- 6.1 Well quasi-orders.- 6.2 Higman’s theorem.- 6.3 The generalized Myhill theorem.- 6.4 Quasi-orders and rewriting systems.- 6.5 A regularity condition for permutable languages.- 6.6 Almost-commutative languages.- 6.7 Copying systems.- References.

Dati bibliografici

Titolo: Finiteness and Regularity in Semigroups and ...
Casa editrice: Springer
Data di pubblicazione: 2011
Legatura: Brossura
Condizione: New