Cyclic terms for SD⋁ varieties revisited

Barto, Libor; Kozik, Marcin

doi:10.1007/s00012-010-0094-z

Algebra Univers.

2010

DOI: 10.1007/s00012-010-0094-z

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Cyclic terms for SD⋁ varieties revisited

Libor Barto

Marcin Kozik

Abstract: Abstract. We present a direct proof showing that every finite algebra generating a congruence join semidistributive variety has a cyclic term.

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2012

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Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

Barto¹,

Kozik²

2012

Logical Methods in Computer Science

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153

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Abstract. The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete otherwise. This paper provides two new characterizations of finitely generated Taylor varieties. The first characterization is using absorbing subalgebras and the second one cyclic terms. These new conditions allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the authors) and the characterization of locally finite Taylor varieties using weak nearunanimity terms (proved by McKenzie and Maróti) in an elementary and self-contained way.

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Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

Barto¹,

Kozik²

2012

Logical Methods in Computer Science

Self Cite

153

View full text Add to dashboard Cite

show abstract

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Cyclic terms for SD⋁ varieties revisited

Abstract: Abstract. We present a direct proof showing that every finite algebra generating a congruence join semidistributive variety has a cyclic term.

Cited by 1 publication

References 5 publications

Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

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