Solving word equations modulo partial commutations

Diekert, Volker; Matiyasevich, Yuri; Muscholl, Anca

doi:10.1016/s0304-3975(98)00313-2

Cited by 19 publications

(14 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we restrict our considerations to the free partially commutative monoid G + of positive words in G, then HNN-normal form of elements in G + coincides with the priority normal form of Matiyasevich [22,51].…”

Section: Normal Forms Arising From Hnn Extensionsmentioning

confidence: 99%

Divisibility theory and complexity of algorithms for free partially commutative groups

Esyp¹,

Kazachkov²,

Remeslennikov³

2005

Contemporary Mathematics

View full text Add to dashboard Cite

Section: Normal Forms Arising From Hnn Extensionsmentioning

confidence: 99%

Divisibility theory and complexity of algorithms for free partially commutative groups

Esyp¹,

Kazachkov²,

Remeslennikov³

2005

Contemporary Mathematics

View full text Add to dashboard Cite

“…, locally free groups [9,28,34] and of course (free) partially commutative groups [3,7,11,12,15,17,18,21,25,27,32]. We refer the reader to [5,13,21,22] for further references, more comprehensive surveys, introductory material and discussion of the various manifestations of these groups.…”

mentioning

confidence: 99%

Parabolic and quasiparabolic subgroups of free partially commutative groups

2007

View full text Add to dashboard Cite

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ , which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

show abstract

“…Another branch of research was to extend Makanin's result to more general algebraic structures including free partially commutative monoids [22,6], free partially commutative monoids with involution, graph groups (also known as right-angled Artin groups) [7], graph products [5], and hyperbolic groups [30,2]. In all these cases the existential theory of equations is decidable.…”

Section: Introductionmentioning

confidence: 99%

Finding all solutions of equations in free groups and monoids with involution

Diekert¹,

Jeż²,

Plandowski³

2016

Information and Computation

Self Cite

View full text Add to dashboard Cite

Abstract. The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented recompression technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutiérrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite. 5

show abstract

Solving word equations modulo partial commutations

Cited by 19 publications

References 20 publications

Divisibility theory and complexity of algorithms for free partially commutative groups

Divisibility theory and complexity of algorithms for free partially commutative groups

Parabolic and quasiparabolic subgroups of free partially commutative groups

Finding all solutions of equations in free groups and monoids with involution

Contact Info

Product

Resources

About