Constructing divisions into power groups
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Turing machines and bimachines
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Information Sciences: an International Journal
On Schützenberger products of semirings
DLT'10 Proceedings of the 14th international conference on Developments in language theory
On properties not inherited by monoids from their Schützenberger groups
Information and Computation
A cascade decomposition of weighted finite transition systems
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Star-free languages are Church-Rosser congruential
Theoretical Computer Science
The Krohn-Rhodes Theorem and Local Divisors
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Iterated periodicity over finite aperiodic semigroups
European Journal of Combinatorics
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Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader - from the graduate student to the researcher/practitioner with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: (1) Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; (2) Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; (3) Introduces spectral theory into finite semigroup theory; (4) Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; (5) Presents over 70 research problems, most new, and hundreds of exercises. Additional features: (1) For newcomers, an appendix on elementary finite semigroup theory; (2) Extensive bibliography and index. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory.