| Born: 1954, Russia |
Academic Qualifications:Ph.D. 1983, Moldavian Academy of science, Kishinev.
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Academic Positions:
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Research Interests:
Semigroup theory. Varieties. Pseudovarieties and collective varieties of universal algebras. Relatively free semigroups.Word problem. Identity problem. Equations in relatively free algebras. Compactness. Unification. |
Research Projects:
The Finite Basis (including Tarski-Sapir) problem forsemigroup identities. Pseudoidentities. Collective identities and polyalphabetic (graduated) identities of semigroups. Unification Type Problem for groups, semigroups and algebras. Compactness Property for semigroup equations. |
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Abstracts of Current Research:- The Finite Basis Problem: namely which systems of semigroup identitiescan be deduced from the finite number of identities.A new methods of proving the existence andnon-existance of finite basis for some classes of semigroup identities weredeveloped and used to find a finite basis of identities for some classes ofsemigroups, matrix semigroups, transformation semigroups. Some of thisresults are generalized to collective varieties.The main application is the Membership Problem, namely find an algorithm(conditions) for given semigroups (objects) to be included in a given classof semigroups (objects). If we consider the membership problem in the maximalgenerality, then we can present any problem in the form of membership problem.This problem seems to be the central problem of `Finite Algoritmic Algebra`.In papers published in 1996-1998 the solution of the Finite BasisProblem implies a solution of the Membership Problem.A new method for solution of the Finite Bases Problem is developing inthe submitted papers.
- Influence of 0-ary operations on properties of algebras: Usually in algebraic applications particularly in computer sciencewe use not only an algebraic system itself but its elements as well.Hence any algebraic expression (equation, identity and so on) can containconstants (coefficients). In this case many important results and methodsbecome wrong. Some of these results particularly wellknown 0-1 principlewere generalized in joint work with M. Codish. Another area of applicationsis the Compactness Property for semigroup equations.
- Unification Problem in Varieties: is one of the central problems oftheoretical computer science and in universal algebraic geometry.Conections between Finite Basis Problem for varietiesUnification Type Problem were invented. It gives an opportunity to describesemigroups of unitary or finitary unification type in many important cases,particularly for finite inverese semigroups and for overcomutative varieties.
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Publications:- Mashevitzky, G. & Schein, B.. Automorphisms of the semigroup of endomorphisms of a free semigroup or a free monoid. Proceedings of AMS : (2001)
- Mashevitzky, G.I.. On a finite basis problem for universal positive formulas. Algebra Universalis 35: 124-140 (2000)
- Mashevitzky, G.I.. On finite basis problem for left hereditary systems of identities. in Semigroups, automata and languages, World Scientific Publisher: 167 - 183 (2000)
- Codish, M. & Mashevitzky, G.I.. Proving implications by algebraic approximation. Theoretical Computer Science 165: 57-74 (1997)
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| Keywords:Semigroup, Semigroup Identity, Finite Basis Problem, Word Problem, Variety, Pseudovariety, Semigroup Equation, Unification, Compactness. |
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Phones:
- Phone: 972-8-6461602
- Fax: 972-8-6472910
- Mobile: 972-50-8754565
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