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Complexity issues of checking identities in finite monoids

2009
*
Semigroup Forum
*

We study the computational

doi:10.1007/s00233-009-9180-y
fatcat:psx6schakndj3e72yhhnht4kka
*complexity**of**checking**identities*in a fixed finite monoid. ... We find the smallest monoid for which this problem is coNPcomplete and describe a significant class*of*finite monoids for which the problem is tractable. ... my language errors and suggestions how to improve the presentation*of*the paper. ...##
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Complexity of the identity checking problem for finite semigroups

2009
*
Journal of Mathematical Sciences
*

We prove that the

doi:10.1007/s10958-009-9397-z
fatcat:qn6axkizirhbxdockdfebpaqhi
*identity**checking*problem in a finite*semigroup*S is co-NP-complete whenever S has a nonsolvable subgroup or S is the*semigroup**of*all transformations on a 3-element set. ... However an investigation*of*the computational*complexity**of*this problem has started only recently and has brought rather unexpected results. ... However, combining Corollary 1 with some known results, one can completely classify some important series*of**semigroups*with respect to the*complexity**of**identity**checking*. ...##
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A Polynomial Time Algorithm for Left [Right] Local Testability
[chapter]

2003
*
Lecture Notes in Computer Science
*

and for

doi:10.1007/3-540-44977-9_19
fatcat:5etk7zvkevht5n7v2cj2tpc7am
*checking*the transition graph*of*the automaton with locally idempotent*semigroup*. ... A*semigroup*is called*semigroup**of*left [right] zeroes if satises the*identity*xy = x [xy = y]. ... (y(n 2 ) time*complexity*). The whole time and space*complexity**of*the algorithm is y(n 2 ). ...##
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Polynomial time algorithm for left [right] local testability
[article]

2020
*
arXiv
*
pre-print

the words

arXiv:2011.04236v1
fatcat:cqqsr4mglfb4zldtlljbkgbx4u
*of*length k coincide, (2) the set*of*segments*of*length k*of*the words as well as 3) the order*of*the first appearance*of*these segments in prefixes [suffixes] coincide. ... Polynomial time algorithm verifies transition graph*of*automaton with locally idempotent transition semi group. ... The whole time and space*complexity**of*the algorithm is O(n 3 ). Γ 2 . (O(n 2 ) time*complexity*). Let us*check*the local idempotency (O(n 3 ) time*complexity*). ...##
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A minimal nonfinitely based semigroup whose variety is polynomially recognizable

2011
*
Journal of Mathematical Sciences
*

We exhibit a 6-element

doi:10.1007/s10958-011-0512-6
fatcat:enlmyvm4krhvtjcircdu7fvxra
*semigroup*that has no finite*identity*basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm. ... The first and the second authors acknowledge support from the Federal Education Agency*of*Russia, project 2.1.1/3537, and from the Russian Foundation for Basic Research, grants 09-01-12142 and 10-01-00524 ... Under the premise*of*the lemma, in order to*check*whether or not a given finite*semigroup*A belongs to the variety var B, it suffices to*check*whether or not A satisfies all*identities*in Σ. ...##
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The Quantum Query Complexity of Algebraic Properties
[article]

2007
*
arXiv
*
pre-print

For a set S and a binary operation on S, we consider the decision problem whether S is a

arXiv:0705.1446v1
fatcat:lrs3hgjszzborl2azodm3wfipy
*semigroup*or has an*identity*element. If S is a monoid, we want to decide whether S is a group. ... We present quantum query*complexity*bounds for testing algebraic properties. ... To*check*whether a pair (A, B) is marked, we search for a pair (b, c) Corollary 3. 2 2 The quantum query*complexity**of*the*semigroup*problem is O(n 5 4 ), if M has constant size.Note that the time*complexity*...##
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Identities of the Kauffman Monoid K_4 and of the Jones monoid J_4
[article]

2019
*
arXiv
*
pre-print

This leads to a polynomial time algorithm to

arXiv:1910.09190v1
fatcat:7mvdt7zvjngljflhw76hgp7y6a
*check*whether a given*identity*holds in K_4. As a byproduct, we also find a polynomial time algorithm for*checking**identities*in the Jones monoid J_4. ... ., are two families*of*monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids K_3 and K_4 satisfy exactly the same*identities*. ... Thus, it remains to compute the numbers*of*circles in ξC ·ηC and in (ξη)C and to verify that these numbers are equal, that is, ξC · ηC = (ξη)C . ...##
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Semigroups embeddable in hyperplane face monoids

2013
*
Semigroup Forum
*

A similar result is obtained for the

doi:10.1007/s00233-013-9542-3
fatcat:5dzo25vulvbynhqlwdd6l7jdcm
*semigroups*embeddable in*complex*hyperplane*semigroups*. ... A finite*semigroup*embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an*identity*to the two-element left zero*semigroup*. ... Acknowledgements The authors would like to thank Igor Dolinka for helpful correspondence on questions related to this paper and Mark Sapir for explaining in detail the results*of*his thesis [32] that ...##
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Semigroups embeddable in hyperplane face monoids
[article]

2012
*
arXiv
*
pre-print

A similar result is obtained for the

arXiv:1212.6683v1
fatcat:u3kbqt5qxzgmnpvxoql2ztlhdi
*semigroups*embeddable in*complex*hyperplane*semigroups*. ... A finite*semigroup*embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an*identity*to the two-element left zero*semigroup*. ... Acknowledgements The authors would like to thank Igor Dolinka for helpful correspondence on questions related to this paper and Mark Sapir for explaining in detail the results*of*his thesis [32] that ...##
###
On the complexity of inverse semigroup conjugacy
[article]

2021
*
arXiv
*
pre-print

We investigate the computational

arXiv:2111.07551v1
fatcat:4ichaz3qbzfw7ilpyb2guj2ic4
*complexity**of*various decision problems related to conjugacy in finite inverse*semigroups*. ... We describe a connection between*checking*~i conjugacy and*checking*membership in inverse*semigroups*. ... Both*of*the following problems are in AC 0 : (a)*checking*if ∼ o is the*identity*relation on S and (b)*checking*if ∼ p * is the*identity*relation on S.Proof. ...##
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Verification Tools for Checking some kinds of Testability
[article]

2021
*
arXiv
*
pre-print

The bounds on order

arXiv:2106.02312v1
fatcat:offfcgrr7rbjjp7y6fhhkhyeou
*of*local testability*of*transition graph and order*of*local testability*of*transition*semigroup*are also found. For given k, the k-testability*of*transition graph is verified. ... A set*of*procedures for deciding whether or not a language given by its minimal automaton or by its syntactic*semigroup*is locally testable, right or left locally testable, threshold locally testable, ... So in*semigroup*case, we have O(22126 2 ) time*complexity*for both*checking*the local testability and finding the order. ...##
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THE COMPLEXITY OF CHECKING IDENTITIES OVER FINITE GROUPS

2006
*
International journal of algebra and computation
*

We analyze the computational

doi:10.1142/s0218196706003256
fatcat:eo5ahy36ajaynioq7gbobb4mui
*complexity**of*solving a single equation and*checking**identities*over finite meta-abelian groups. ... Among others we answer a question*of*Goldmann and Russel from '98: We prove that it is decidable in polynomial time whether or not an equation over the six element group S 3 has a solution. ... Szabó, The computational*complexity**of**checking*identites in simple*semigroups*and matrix*semigroups*over finite fields,*Semigroup*Forum (2002) [11] P. Tesson, D. ...##
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A Package TESTAS for Checking Some Kinds of Testability
[chapter]

2003
*
Lecture Notes in Computer Science
*

The bounds on order

doi:10.1007/3-540-44977-9_22
fatcat:ipajbwiuqrciha6xmnnhqcl6nq
*of*local testability*of*transition graph and order*of*local testability*of*transition*semigroup*are also found. For given k, the k-testability*of*transition graph is veried. ... We implement a set*of*procedures for deciding whether or not a language given by its minimal automaton or by its syntactic*semigroup*is locally testable, right or left locally testable, threshold locally ... The graphs*of*automata with locally idempotent transition*semigroup*are*checked*too (y(n 3 ) time*complexity*). ...##
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On the Complexity of Properties of Transformation Semigroups
[article]

2019
*
arXiv
*
pre-print

Moreover, we show how to compute left and right

arXiv:1811.00060v2
fatcat:l4hopup5ubfodbteg4gqwdwx54
*identities**of*a transformation*semigroup*in polynomial time. Finally, we show that*checking*whether an element is regular is PSPACE-complete. ... We investigate the computational*complexity*for determining various properties*of*a finite transformation*semigroup*given by generators. ... See [1] for background and*complexity*results on*identity**checking*; in particular, examples*of**semigroups*for which it is coNP-complete. ...##
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A Note on Complex Algebras of Semigroups
[chapter]

2004
*
Lecture Notes in Computer Science
*

The main result is that the variety generated by

doi:10.1007/978-3-540-24771-5_15
fatcat:j67dj6ishvhuvkudkcgnrfulpa
*complex*algebras*of*(commutative)*semigroups*is not finitely based. ... It is shown that this variety coincides with the variety generated by*complex*algebras*of*partial (commutative)*semigroups*. ... . , A 11 can be embedded in*complex*algebras*of*finite*semigroups*. ...
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