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Towards parametrizing word equations

H. Abdulrab, P. Goralčík, G. S. Makanin (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Classically, in order to resolve an equation u ≈ v over a free monoid X * , we reduce it by a suitable family ℱ of substitutions to a family of equations u f ≈ v f , f ∈ ℱ , each involving less variables than u ≈ v , and then combine solutions of u f ≈ v f into solutions of u ≈ v . The problem is to get ℱ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v . We carry out such a parametrization in the case the prime equations in the graph...

Towards parametrizing word equations

H. Abdulrab, P. Goralčík, G. S. Makanin (2010)

RAIRO - Theoretical Informatics and Applications

Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family ℱ of substitutions to a family of equations uf ≈ vf, f ∈ ℱ , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get ℱ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the...

Transformation semigroups associated to Γ-semigroups

Dariush Heidari, Marzieh Amooshahi (2013)

Discussiones Mathematicae - General Algebra and Applications

The concept of Γ-semigroups is a generalization of semigroups. In this paper, we associate two transformation semigroups to a Γ-semigroup and we call them the left and right transformation semigroups. We prove some relationships between the ideals of a Γ-semigroup and the ideals of its left and right transformation semigroups. Finally, we study some relationships between Green's equivalence relations of a Γ-semigroup and its left (right) transformation semigroup.

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