DECIDING SOME MALTSEV CONDITIONS IN FINITE IDEMPOTENT ALGEBRAS

MALTSEV CONDITIONS FOR GENERAL CONGRUENCE MEET-SEMIDISTRIBUTIVE ALGEBRAS

Journal of Symbolic Logic ◽

10.1017/jsl.2021.14 ◽

2021 ◽

pp. 1-20

Author(s):

MIROSLAV OLŠÁK

Keyword(s):

Maltsev Conditions

Download Full-text

Simpler Maltsev conditions for (weak) difference terms in locally finite varieties

Algebra Universalis ◽

10.1007/s00012-017-0475-7 ◽

2017 ◽

Vol 78 (4) ◽

pp. 555-561 ◽

Cited By ~ 1

Author(s):

Keith A. Kearnes ◽

Ágnes Szendrei ◽

Ross Willard

Keyword(s):

Locally Finite ◽

Maltsev Conditions ◽

Locally Finite Varieties

Download Full-text

Hardness results for the subpower membership problem

International Journal of Algebra and Computation ◽

10.1142/s0218196718500339 ◽

2018 ◽

Vol 28 (05) ◽

pp. 719-732

Author(s):

Jeff Shriner

Keyword(s):

Finite Algebra ◽

Membership Problem ◽

Finite Algebras ◽

Maltsev Condition ◽

Cube Term ◽

Maltsev Conditions ◽

Congruence Distributive

The main result of this paper shows that if [Formula: see text] is a consistent strong linear Maltsev condition which does not imply the existence of a cube term, then for any finite algebra [Formula: see text] there exists a new finite algebra [Formula: see text] which satisfies the Maltsev condition [Formula: see text], and whose subpower membership problem is at least as hard as the subpower membership problem for [Formula: see text]. We characterize consistent strong linear Maltsev conditions which do not imply the existence of a cube term, and show that there are finite algebras in varieties that are congruence distributive and congruence [Formula: see text]-permutable ([Formula: see text]) whose subpower membership problem is EXPTIME-complete.

Download Full-text

ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS

International Journal of Algebra and Computation ◽

10.1142/s0218196709004956 ◽

2009 ◽

Vol 19 (01) ◽

pp. 41-77 ◽

Cited By ~ 16

Author(s):

RALPH FREESE ◽

MATTHEW A. VALERIOTE

Keyword(s):

Polynomial Time ◽

Finite Algebra ◽

Free Algebras ◽

Congruence Distributivity ◽

Sharp Bounds ◽

Polynomial Time Algorithms ◽

Maltsev Conditions

This paper studies the complexity of determining if a 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. In addition, we provide sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.

Download Full-text