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Inverse semigroups with rational word problem are finite
[article]

2013
*
arXiv
*
pre-print

*The*notion of

*word*

*problem*used is

*the*

*two*-tape

*word*

*problem*--

*the*set of all pairs of

*words*over a

*generating*set

*for*

*the*

*semigroup*which both represent

*the*same element. ... This note proves a generalisation to inverse

*semigroups*of Anisimov's theorem that a group has regular

*word*

*problem*if and only if it is finite, answering a question of Stuart Margolis. ... Acknowledgement

*The*author was funded by an EPSRC grant EP/H011978/1. ...

##
###
Deciding Word Problems of Semigroups using Finite State Automata
[article]

2019
*
arXiv
*
pre-print

We explore a natural class of

arXiv:1206.1714v4
fatcat:hykz5kzhvrg4fhkbsocu3darq4
*semigroups*that have*word**problem*decidable by finite state automata. ... Among*the*main results are invariance of this property under change of*generators*, invariance under basic algebraic constructions and algebraic properties of these*semigroups*. ... This*problem*is commonly called*the**word**problem*, and is undecidable in*general*: There are examples of*semigroup*presentations*for*which there is no algorithm that decides*the**word**problem*. ...##
###
Word problem languages for completely regular semigroups
[article]

2020
*
arXiv
*
pre-print

that is a union of finitely many finitely

arXiv:2003.13608v1
fatcat:ulhbqril6na6ngfzqwle6fzs4m
*generated*groups*with**word**problem*in C also has*word**problem*in C. ... Motivated by*the*question of which completely regular*semigroups*have context-free*word**problem*, we show that*for*certain classes of languages C(including context-free), every completely regular*semigroup*...*The*author is grateful to Alan Cain*for*helpful discussions, and particularly*for**the*trick*with**the*idempotents. ...##
###
A note on decidability questions on presentations of word semigroups

1997
*
Theoretical Computer Science
*

*With*each F-

*semigroup*we associate an F-presentation, which turns out to be finite

*for*all finitely

*generated*F-

*semigroups*. ... It is also shown that it is undecidable whether

*two*finitely

*generated*F-

*semigroups*satisfy a common relation in their F-presentations. ...

*The*isomorphism

*problem*

*for*finitely

*generated*F-

*semigroups*is decid-Proof. Let A+ and B+ be

*two*F-

*semigroups*. ...

##
###
Uniform decision problems for automatic semigroups

2006
*
Journal of Algebra
*

*With*mild restrictions on

*the*automatic structure, which are necessary to make

*the*

*problem*well defined,

*the*uniform

*word*

*problem*

*for*

*semigroups*described by automatic structures is decidable. ...

*the*

*semigroup*, in

*the*form of a Rees matrix together

*with*an automatic structure

*for*its maximal subgroup. ... Acknowledgment

*The*first author thanks Kirsty

*for*all her support and encouragement. ...

##
###
Minsky machines and algorithmic problems
[article]

2015
*
arXiv
*
pre-print

This is a survey of using Minsky machines to study algorithmic

arXiv:1504.07736v1
fatcat:fwlcnaishbcgfhtbw4snzhooim
*problems*in*semigroups*, groups and other algebraic systems. ...*The*uniform*word**problem**for*finite*semigroups*Let L be a finite conjunction of equalities u = v, where u, v are*words*in some alphabet X. Let U, V be*two**words*in X. ... That result turned out to be influential*for**two*reasons. First, it opened*the*area of studying*the*uniform*word**problem*in several classes of algebras, including*semigroups*and groups. ...##
###
Page 1982 of Mathematical Reviews Vol. 52, Issue 6
[page]

1976
*
Mathematical Reviews
*

*The*author concerns himself

*with*

*the*reduction of

*the*

*word*

*problem*

*for*finitely presented

*semigroups*to that of

*the*associa- tivity

*problem*

*for*finite monoids. ... Tamari, Dov 14098

*The*associativity

*problem*

*for*monoids and

*the*

*word*

*problem*

*for*

*semigroups*and groups. ...

##
###
Uniform decision problems in automatic semigroups
[article]

2005
*
arXiv
*
pre-print

*With*mild restrictions on

*the*automatic structure, which seem to be necessary to make

*the*

*problem*well-defined,

*the*uniform

*word*

*problem*

*for*

*semigroups*described by automatic structures is decidable. ...

*the*

*semigroup*, in

*the*form of a Rees matrix together

*with*an automatic structure

*for*its maximal subgroup. ...

*The*first author would like to thank Kirsty

*for*all her support and encouragement. ...

##
###
Anisimov's Theorem for inverse semigroups
[article]

2013
*
arXiv
*
pre-print

*The*idempotent

*problem*of a finitely

*generated*inverse

*semigroup*is

*the*formal language of all

*words*over

*the*

*generators*representing idempotent elements. ... This note proves that a finitely

*generated*inverse

*semigroup*

*with*regular idempotent

*problem*is necessarily finite. ... Acknowledgements

*The*author thanks Tara Brough, Marianne Johnson and Markus Pfeiffer

*for*helpful conversations. ...

##
###
Page 756 of Mathematical Reviews Vol. , Issue 2004b
[page]

2004
*
Mathematical Reviews
*

*The*

*word*

*problem*Wy(G) of a finitely

*generated*group G

*with*respect to

*the*

*generating*set U is

*the*language {u € (UUU7~')* u =g 1}. ...

*The*results outlined above correspond to

*the*special case of only

*two*layers, one

*for*

*the*

*words*

*with*v and one

*for*

*the*others. ...

##
###
Anisimov's Theorem for inverse semigroups

2015
*
International journal of algebra and computation
*

*The*idempotent

*problem*of a finitely

*generated*inverse

*semigroup*is

*the*formal language of all

*words*over

*the*

*generators*representing idempotent elements. ... This note proves that a finitely

*generated*inverse

*semigroup*

*with*regular idempotent

*problem*is necessarily finite. ... Acknowledgements

*The*author thanks Tara Brough, Marianne Johnson and Markus Pfeiffer

*for*helpful conversations. ...

##
###
A simple presentation of a group with unsolvable word problem

1986
*
Illinois Journal of Mathematics
*

*The*

*word*

*problem*

*for*G (XIR) is

*the*

*problem*of deciding when

*two*

*words*u and v lie in

*the*same equivalence class--in symbols--when u = v. ...

*The*transition from an individual

*word*

*problem*

*for*a

*semigroup*presentation to

*the*

*word*

*problem*

*for*a group presentation is

*the*basis of Boone's construction [1] , [2] and

*the*example we give relies ...

##
###
Page 248 of Mathematical Reviews Vol. 34, Issue 2
[page]

1967
*
Mathematical Reviews
*

*The*author solves

*the*

*word*

*problem*

*for*finitely presented commutative

*semigroups*

*with*

*two*

*generators*. R. J. Warne (Morgantown, W. Va.) Birjukov, A. ... P. 1422 Solvability of

*the*

*problem*of isomorphism

*for*finitely defined commutative

*semigroups*

*with*

*two*

*generators*. (Russian) Interuniv. Sci. Sympos.

*General*Algebra (Russian), pp. 5-6. Tartu. Gos. ...

##
###
Matrix Semigroup Freeness Problems in SL(2,Z)
[article]

2016
*
arXiv
*
pre-print

In other

arXiv:1610.09834v1
fatcat:owrw3ypdgjfahhko7ysl6xwkde
*words*, is G a code? We show that*the**problem*of deciding whether a matrix*semigroup*in SL(2,Z) is non-free is NP-hard. ... In particular, we study*the*freeness*problem*: given a finite set of matrices G*generating*a multiplicative*semigroup*S, decide whether each element of S has at most one factorization over G. ... Indeed,*the*freeness*problem**for*matrix*semigroups**with*a single*generator*is*the*complementary*problem*of*the*matrix torsion*problem*which asks whether there exist*two*integers p, q ≥ 1 such that M p ...##
###
On the word problem for the free Burnside semigroups satisfying x 2 = x 3

2011
*
Russian Mathematics (Izvestiya VUZ. Matematika)
*

*For*any k > 2, we reduce this

*problem*

*for*

*the*k-

*generated*free Burnside

*semigroup*B(2, 1, k) to

*the*

*word*

*problem*

*for*

*the*

*two*-

*generated*

*semigroup*B (2, 1, 2) . ... We study

*the*

*word*

*problem*

*for*

*the*free Burnside

*semigroups*satisfying x 2 = x 3 . ...

*The*

*word*

*problem*

*for*a

*semigroup*B(2, 1, k)

*with*k > 2 is solvable if and only if it is solvable

*for*

*the*

*semigroup*B(2, 1, 2). * E-mail: mathplush@yandex.ru. ...

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