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Deciding some Maltsev conditions in finite idempotent algebras
[article]

2019
*
arXiv
*
pre-print

*In*this paper we investigate the computational complexity of

*deciding*if a given

*finite*

*algebraic*structure satisfies a fixed (strong)

*Maltsev*

*condition*Σ. ... Our goal

*in*this paper is to show that Σ-testing can be accomplished

*in*polynomial time when the

*algebras*tested are

*idempotent*and the

*Maltsev*

*condition*Σ can be described using paths. ... Path

*Maltsev*

*conditions*

*In*this section, we will show how to express several classical

*Maltsev*

*conditions*using paths and how to efficiently

*decide*them

*in*

*finite*

*idempotent*

*algebras*by checking that they ...

##
###
Deciding the existence of minority terms
[article]

2019
*
arXiv
*
pre-print

This paper investigates the computational complexity of

arXiv:1901.00316v2
fatcat:b5hybyqzujfcpcdnpq7p57mzbu
*deciding*if a given*finite**idempotent**algebra*has a ternary term operation m that satisfies the minority equations m(y,x,x) ≈ m(x,y,x) ≈ m(x,x,y) ... We show that a common polynomial-time approach to testing for this type of*condition*will not work*in*this case and that this decision problem lies*in*the class NP. ... Local*Maltsev*terms*In*[5, 7, 8, 13] polynomial-time algorithms are presented for*deciding*if certain*Maltsev**conditions*hold*in*the variety generated by a given*finite**idempotent**algebra*. ...##
###
Algebras and Algorithms

2015
*
2015 IEEE International Symposium on Multiple-Valued Logic
*

When considering computational questions for

doi:10.1109/ismvl.2015.45
dblp:conf/ismvl/Valeriote15
fatcat:3eja6v2wvvamre4t6st32us7fm
*finite**algebras*we further assume that they have a*finite*number of basic operations. ... Two*algebras*are similar if their basic operations are indexed by the same set and the arities of similarly indexed operations are the same. A is a*finite**algebra*if its universe is a*finite*set. ...*Some*types of*idempotent**Maltsev**conditions*are easier to test for over*idempotent**algebras*. ...##
###
Deciding the existence of quasi weak near unanimity terms in finite algebras
[article]

2021
*
arXiv
*
pre-print

We also observe that the problem of

arXiv:2002.06083v3
fatcat:ntok5sh2sjgi3i4nh42j36dmlq
*deciding*if a given*finite**algebra*has a quasi Taylor operation is solvable*in*polynomial time by looking, essentially, for local quasi Siggers operations. ... We show that for a fixed positive integer k one can efficiently*decide*if a*finite**algebra*A admits a k-ary weak near unanimity operation by looking at the local behavior of the terms of A. ... This is*in*contrast to the numerous examples of*idempotent**Maltsev**conditions*that are EXPTIME-complete to*decide**in*general*finite**algebras*[7, 9] . ...##
###
The local-global property for G-invariant terms
[article]

2021
*
arXiv
*
pre-print

For

arXiv:2109.02065v2
fatcat:sgqbk5xrw5ekldtopmf3wtgl34
*some**Maltsev**conditions*Σ it is enough to check if a*finite**algebra*𝐀 satisfies Σ locally on subsets of bounded size,*in*order to*decide*, whether 𝐀 satisfies Σ (globally). ... This local-global property is the main known source of tractability results for*deciding**Maltsev**conditions*. ... Acknowledgements We thank Matt Valeriote for suggesting the question of studying the*conditions*Σ . ...##
###
Equations implying congruence n-permutability and semidistributivity

2013
*
Algebra Universalis
*

*In*this paper we investigate other types of derivatives that give similar results for congruence n-permutable for

*some*n, and for congruence semidistributivity. ...

*In*[3] T. Dent, K. Kearnes andÁ. Szendrei define the derivative, Σ , of a set of equations Σ and show, for

*idempotent*Σ, that Σ implies congruence modularity if Σ is inconsistent (Σ |= x ≈ y). ... (The Day terms work.) (3) The converse of the first statement is not true

*in*general but it is true if Σ is linear. (4) For a

*finite*linear,

*idempotent*Σ one can effectively

*decide*if Σ implies CM. ...

##
###
A new algorithm for constraint satisfaction problems with Maltsev templates
[article]

2017
*
arXiv
*
pre-print

*In*this article, we provide a new algorithm for solving constraint satisfaction problems with

*Maltsev*constraints, based on the new notion of

*Maltsev*consistency. ... Simple

*Idempotent*

*Algebras*

*in*

*Maltsev*Varieties. Let A be an

*algebra*. ... [15] ) and is closely related to modules over rings of matrices whose entries come from

*some*fixed

*finite*field: A

*finite*

*idempotent*Abelian

*algebra*A is strictly simple if and only if there exist a ...

##
###
Asking the metaquestions in constraint tractability
[article]

2017
*
arXiv
*
pre-print

Among other results, we prove the NP-completeness of

arXiv:1604.00932v2
fatcat:lxq7lwrs2jb3hiajsjrss6klny
*deciding*a*condition*conjectured to characterize the tractable problems CSP(H), as well as the NP-completeness of*deciding*if CSP(H) has bounded width ... The CSP is*in*general NP-hard; a common way to restrict this problem is to fix the second structure H, so that each structure H gives rise to a problem CSP(H). ... A strong linear*Maltsev**condition*is a*finite*set of linear identities {E 1 , . . . , E r }. ...##
###
Simpler Maltsev conditions for (weak) difference terms in locally finite varieties

2017
*
Algebra Universalis
*

This paper is motivated by a practical question: given a

doi:10.1007/s00012-017-0475-7
fatcat:efrbbwwwyfabnlud3xziovxs7y
*finite**algebra*A*in*a*finite*language, how can we best program a computer to*decide*whether the variety generated by A has a di↵erence term, and ... To help address this question we produce a simple*Maltsev**condition*which characterizes di↵erence terms*in*the class of locally*finite*varieties. We do the same for weak di↵erence terms. ... Simple*Maltsev**conditions*Following [5, Def. 5.2] , given congruences ↵, , of an*algebra*, define ⌧ (↵, , ) to be the transitive closure of [ (↵ \ ( (↵ \ ) )). ...##
###
SOLVABILITY OF SYSTEMS OF POLYNOMIAL EQUATIONS OVER FINITE ALGEBRAS

2007
*
International journal of algebra and computation
*

By developing the underlying idea further, we present a dichotomy theorem

doi:10.1142/s0218196707003809
fatcat:4clxdhuqlzdrzabgqhkygwda2m
*in*the class of*finite**algebras*that admit a non-trivial*idempotent**Maltsev**condition*. ... We prove that the problem has a dichotomy*in*the class of*finite*groupoids with an identity element. ... Admitting a non-trivial*idempotent**Maltsev**condition*is a*decidable*property of*finite**algebras*of*finite*signature, see [6] , and is even*in*P*in*the case of*idempotent**algebras*, as shown*in*[1] . ...##
###
ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS

2009
*
International journal of algebra and computation
*

This paper studies the complexity of determining if a

doi:10.1142/s0218196709004956
fatcat:tktlwduwabg2diycwowd3cbwzm
*finite**algebra*generates a variety that satisfies various*Maltsev**conditions*, such as congruence distributivity or modularity. ... For*idempotent**algebras*we show that there are polynomial time algorithms to test for these*conditions*but that*in*general these problems are EXPTIME complete. ... If A is a*finite**idempotent**algebra*and i ∈ typ(V(A)) then there is a*finite*strictly simple*algebra*S of type j for*some*j ≤ i*in*H S(A). ...##
###
Polynomial-Time Tests for Difference Terms in Idempotent Varieties

2019
*
International journal of algebra and computation
*

We consider the following practical question: given a

doi:10.1142/s021819671950036x
fatcat:p5wehl2zj5b27ckcc3qgfw5nui
*finite**algebra*A*in*a*finite*language, can we efficiently*decide*whether the variety generated by A has a difference term? ... We answer this question (positively)*in*the*idempotent*case and then describe algorithms for constructing difference term operations. ... If A is a*finite**idempotent**algebra*and i ∈ typ(V(A)) then there is a*finite*strictly simple*algebra*S of type j for*some*j i*in*HS(A). ...##
###
Random Models of Idempotent Linear Maltsev Conditions. I. Idemprimality
[article]

2019
*
arXiv
*
pre-print

We extend a well-known theorem of Murskiǐ to the probability space of

arXiv:1901.06316v1
fatcat:674bmhcapzccbapaniehujbrci
*finite*models of a system M of identities of a strong*idempotent*linear*Maltsev**condition*. ... This implies that even if such an M is distinguishable from another*idempotent*linear*Maltsev**condition*by a*finite*model A of M, a random search for a*finite*model A of M with this property will almost ... Idemprimality for random*finite*models of*some*familiar strong*idempotent*linear*Maltsev**conditions*∼*in*the last column of the table. ...##
###
Decidability of absorption in relational structures of bounded width

2014
*
Algebra Universalis
*

Absorption theory of Barto and Kozik has proven to be a very useful tool

doi:10.1007/s00012-014-0283-2
fatcat:7vxge3redfgi7b5xdgz5ddwlyq
*in*the*algebraic*approach to the Constraint Satisfaction Problem and structure of*finite**algebras**in*general. ... We address the following problem: Given a*finite*relational structure A and a subset B ⊆ A, is it*decidable*whether B is an absorbing subuniverse? ... Acknowledgements The author would like to thank Libor Barto and Marcin Kozik for their thoughtful comments and helpful discussions and the anonymous reviewer for pointing out an error*in*the manuscript ...##
###
Testing for a Semilattice Term

2018
*
Order
*

Introduction Many of the poly-time algorithms for testing for the satisfaction of a fixed special

doi:10.1007/s11083-018-9455-6
fatcat:spz7ifi7brdpjjwevurfi6akby
*Maltsev**condition**in*a given*finite**idempotent**algebra*involve checking if there are enough "local versions ... The problem of*deciding*if, given a*finite**idempotent**algebra*A and an element 0 ∈ A, that the*condition*from the previous Lemma holds for A and 0 is*in*P . Proof. ...
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