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The word problem for free adequate semigroups

Mark Kambites, Alexandr Kazda
2014 International journal of algebra and computation  
We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids.  ...  holds in the classes of left, right and/or two-sided adequate semigroups.  ...  They also thank Victoria Gould for some helpful comments on the draft, and Stuart Margolis for pointing them to the work of Lohrey and Ondrusch [11] .  ... 
doi:10.1142/s0218196714500404 fatcat:qzk4qf7dujeohbq3ehw6zkp3py

The word problem for free adequate semigroups [article]

Mark Kambites, Alexandr Kazda
2013 arXiv   pre-print
We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids.  ...  holds in the classes of left, right and/or two-sided adequate semigroups.  ...  They also thank Victoria Gould for some helpful comments on the draft, and Stuart Margolis for pointing them to the work of Lohrey and Ondrusch [11] .  ... 
arXiv:1311.7523v1 fatcat:opgv3kt7rjhqjebisbeeddugse

Page 4166 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
In the present paper the author also presents results on the word problem for free objects in certain varieties of bands, on quasivarieties of bands, and on the lattices of varieties of band monoids, *  ...  The re- mainder of the paper consists of miscellany: situations where the distributive law holds are considered and_the solution of the word problem is given for the free objects in OBG, where OBG is the  ... 

Page 4843 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
The word problems for semigroups, cancellative semigroups and finite semigroups are known to be undecidable.  ...  The authors formulate the notion of a finite cancellative semigroup with zero [cf. the paper under review for a precise definition] and show that the word problem for these semigroups is also undecidable  ... 

Page 1420 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
Oxford Ser. (2) 28 (1977), no. 111, 285-300; MR 56 #15811; “Free right h-adequate and free right type A semigroups”, to appear].”  ...  [Determining the rank of an equation in the free monoid] Theoret. Comput. Sci. 16 (1981), no. 3, 337-340. For A a finite alphabet, A* will denote the free monoid over A and | the empty word.  ... 

Page 2747 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
No. 2 (1970), 276-289; MR 52 #14100] we solved the word problem and the isomorphism problem for finitely presented semigroups of class K.  ...  The solution of the problem of occurrence for semigroups belonging to K is unknown to the author. Here we give a solution of the problem of occurrence in a monogenic subsemigroup.”  ... 

FREE ADEQUATE SEMIGROUPS

MARK KAMBITES
2011 Journal of the Australian Mathematical Society  
The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial 'folding' operation which transforms our trees into Munn trees  ...  word problem. 2010 Mathematics subject classification: primary 20M10; secondary 08A10, 08A50.  ...  Gray for pointing out the connection between pruned trees and cores of graphs, and M. V. Lawson for alerting him to the existence of work on free restriction categories [2] .  ... 
doi:10.1017/s1446788711001753 fatcat:zzcg6jhjdnf6fovwk4v4zktrbq

Free right type A semigroups

John Fountain
1991 Glasgow Mathematical Journal  
Among other things we have that Green's relations on A x are trivial, the word problem for A x is solvable and A x is residually finite.  ...  On any right adequate semigroup, there is a minimum right type A congruence and if y is this congruence on P x , the free right h-adequate semigroup on X, then P x ly is the free right type A semigroup  ...  The class si of right type A semigroups is contained in the class of right h-adequate semigroups and so, in the terminology of [15] , P x is free for sd over X, that is, P x is generated by X and, for  ... 
doi:10.1017/s0017089500008168 fatcat:upinkr7grrabnehbd5phqxxqz4

Free adequate semigroups [article]

Mark Kambites
2009 arXiv   pre-print
word problem.  ...  The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial "folding" operation which transforms our trees into Munn trees  ...  Gray for pointing out the connection between pruned trees and cores of graphs, and Mark Lawson for alerting him to the existence of work on free restriction categories [2] .  ... 
arXiv:0902.0297v3 fatcat:l2ohb4fzybflnctcy5w2eny2au

An Approximate Method for Calculating the Distance Between Regular Languages for Multitape Finite Automata

Tigran Grigoryan
2020 Mathematical Problems of Computer Science  
Sets of word tuples, accepted by multitape finite automata and a metric space for languages accepted by these automata, are considered.  ...  These languages are represented using the same notation as the known notation of regular expressions for languages accepted by one-tape automata.  ...  The investigation of this metric shows that in most cases the evaluated distance of the words over a free partially commutative semigroup is adequate, however, after applying the homomorphism K • N um  ... 
doi:10.51408/1963-0060 fatcat:uuejdkvt2bbejkidnucuzt6s5m

Page 4228 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
(RS-URAL) Weak word problem for finite semigroups. Monoids and semigroups with applications (Berkeley, CA, 1989), 206-219, World Sci. Publishing, River Edge, NJ, 1991.  ...  The main positive result concerns two presentations (X,;R,) and (X2;R2) for a semigroup Q which are C(2) and are free of trivial relators and of avoidable letters.  ... 

Retracts of trees and free left adequate semigroups

Mark Kambites
2011 Proceedings of the Edinburgh Mathematical Society  
The class of all such trees (with a fixed labelling alphabet) has an algebraic interpretation, as a free object in the class of adequate semigroups.  ...  Through this correspondence we establish some structural and algorithmic properties of free left adequate semigroups and monoids, and consequently of the category of all left adequate semigroups.  ...  him to the existence of work on free restriction categories [2] , and the anonymous referee for careful reading of the first draft.  ... 
doi:10.1017/s0013091509001230 fatcat:fh6jpzwcy5cypbgcy6karknxke

Page 822 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
The proof is based on a solution of the word problem for e-free objects in CR(H), which is analogous to that for free completely regular semigroups due to J. Kadourek and L.  ...  The model presented for EF(C,,CR(H))y generalizes the reviewer's model [Semigroup Forum 52 (1996), no. |, 61—82] for e- free E-solid semigroups. O Maria B.  ... 

Free left and right adequate semigroups [article]

Mark Kambites
2009 arXiv   pre-print
In this paper we show that there are natural embeddings of each free right adequate and free left adequate semigroup or monoid into the corresponding free adequate semigroup or monoid.  ...  The corresponding classes of trees are easily described and the resulting geometric representation of free left adequate and free right adequate semigroups is even easier to understand than that in the  ...  Mark Lawson for alerting him to the existence of work on free restriction categories [2] .  ... 
arXiv:0904.0916v2 fatcat:5psayozxovbhnm3yhoomjcu4tm

On the model checking of finite state transducers over semigroups
О верификации конечных автоматов-преобразователей над полугруппами

A.R. Gnatenko, V.A. Zakharov
2018 Proceedings of the Institute for System Programming of RAS  
In this paper, we study the verification problem for the programs of this kind. We use finite state transducers over semigroups as formal models of reactive systems.  ...  For citation: Gnatenko A.R., Zakharov V.A. On the model checking of finite state transducers over semigroups. Trudy ISP RAN/Proc. . On the model checking of finite state transducers over semigroups.  ...  Acknowledgments The authors of the article thank the anonymous reviewers for their valuable comments and advice on improving the article.  ... 
doi:10.15514/ispras-2018-30(3)-21 fatcat:2j6ccodla5dkzcxn6bhpmj4g6u
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