In this thesis, we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating the irreducible representations of an inverse semigroup, and we use this method to prove that the problem of creating FFTs for inverse semigroups can ...

We introduce semidirect and wreath products of finite ordered semigroups and extend some standard decomposition results to this case.

In “Sverdlovsk notebook” (Sverdlovsk, 1969), I proposed a question: Are any too first-order equivalent finitely generated commutative semigroups isomorphic? In 1970, B.I.Zilber answered the question negatively. A question arises: In what language, any equivalent over the language finitely generated commutative semigroups are isomorphic? In the note, we propose such a language. Moreover, we prov...

The algebraic study of formal languages draws the equivalence between ω-regular languages and subsets of finite ω-semigroups. The ω-regular languages being the ones characterised by second order monadic formulas. Within this framework, in [1]we provide a characterisation of the algebraic counterpart of the Wagner hierarchy: a celebrated hierarchy of ω-regular languages. For this, we adopt a hie...

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We consider the descriptional complexity of various constructions for weakly recognizing morphisms. This includes the conversion f...