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Inverse semigroups with rational word problem are finite [article]

Tara Brough
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.  ... 
arXiv:1311.3955v1 fatcat:axrqbfm5nfbwdao3elrmmh67j4

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

Max Neunhöffer, Markus Pfeiffer, Nik Ruskuc
2019 arXiv   pre-print
We explore a natural class of 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.  ... 
arXiv:1206.1714v4 fatcat:hykz5kzhvrg4fhkbsocu3darq4

Word problem languages for completely regular semigroups [article]

Tara Brough
2020 arXiv   pre-print
that is a union of finitely many finitely 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.  ... 
arXiv:2003.13608v1 fatcat:ulhbqril6na6ngfzqwle6fzs4m

A note on decidability questions on presentations of word semigroups

C. Choffrut, T. Harju, J. Karhumäki
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.  ... 
doi:10.1016/s0304-3975(96)00311-8 fatcat:vq5pkyghxrazpdmxg6xml5sjvm

Uniform decision problems for automatic semigroups

Mark Kambites, Friedrich Otto
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.  ... 
doi:10.1016/j.jalgebra.2005.11.028 fatcat:xi5eeodke5bfhjplqmo6huju5i

Minsky machines and algorithmic problems [article]

Mark Sapir
2015 arXiv   pre-print
This is a survey of using Minsky machines to study algorithmic 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.  ... 
arXiv:1504.07736v1 fatcat:fwlcnaishbcgfhtbw4snzhooim

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]

Mark Kambites, Friedrich Otto (Universitaet Kassel)
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.  ... 
arXiv:math/0509349v1 fatcat:enr5u4itzva2habo72uox25x2q

Anisimov's Theorem for inverse semigroups [article]

Mark Kambites
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.  ... 
arXiv:1303.5239v1 fatcat:wjwbg4eizfactgx733udd4w2di

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

Mark Kambites
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.  ... 
doi:10.1142/s0218196715400032 fatcat:ezuh2fznubc6nd6knmcl4hbjna

A simple presentation of a group with unsolvable word problem

Donald J. Collins
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  ... 
doi:10.1215/ijm/1256044631 fatcat:nzojwwhlrvdmhdtodkaelkemh4

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]

Sang-Ki Ko, Igor Potapov
2016 arXiv   pre-print
In other 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  ... 
arXiv:1610.09834v1 fatcat:owrw3ypdgjfahhko7ysl6xwkde

On the word problem for the free Burnside semigroups satisfying x 2 = x 3

A. N. Plyushchenko
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.  ... 
doi:10.3103/s1066369x11110119 fatcat:lwqopkbuobhpfd4g7yxzg4uyvm
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