Idempotent n‐permutable varieties

One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n-permutable for some n .I n this paper, we prove two results: (1) for every n> 1, there is a polynomial-time algorithm that, given a finite idempotent algebra A in a finite language, determines whether the variety generated by A is n-permutable and (2) a variety is npermutable for some n if and only if it interprets an idempotent variety that is not interpretable in the variety of distributive lattices.

[1]  Nicole Fassbinder.  Structure Of Finite Algebras Contemporary Mathematics , 2016 .

[2]  Libor Barto,et al.  Constraint Satisfaction Problems Solvable by Local Consistency Methods , 2014, JACM.

[3]  Neil D. Jones,et al.  Complete problems for deterministic polynomial time , 1974, STOC '74.

[4]  Giora Slutzki,et al.  Computational Complexity of Term-Equivalence , 1999, Int. J. Algebra Comput..

[5]  Jonah Horowitz.  Computational Complexity of Various Mal'cEV conditions , 2013, Int. J. Algebra Comput..

[6]  Walter Taylor,et al.  The Lattice of Interpretability Types of Varieties , 1984 .

[7]  Keith A. Kearnes,et al.  The Shape of Congruence Lattices , 2013 .

[8]  Max L. Warshauer,et al.  Lecture Notes in Mathematics , 2001 .

[9]  R. McKenzie,et al.  Algebras, Lattices, Varieties , 1988 .

[10]  Pascal Tesson,et al.  Universal algebra and hardness results for constraint satisfaction problems , 2007, Theor. Comput. Sci..

[11]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[12]  C. Bergman,et al.  Universal Algebra: Fundamentals and Selected Topics , 2011 .

[13]  Ralph Freese,et al.  On the Complexity of Some Maltsev Conditions , 2009, Int. J. Algebra Comput..

[14]  W. Taylor.  Varieties Obeying Homotopy Laws , 1977, Canadian Journal of Mathematics.

[15]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[16]  D. Hobby,et al.  The structure of finite algebras , 1988 .

[17]  George Grätzer,et al.  Two Mal'cev-type theorems in universal algebra , 1970 .

[18]  J. Hagemann,et al.  Onn-permutable congruences , 1973 .

[19]  Jonah Horowitz,et al.  RESULTS ON THE COMPUTATIONAL COMPLEXITY OF LINEAR IDEMPOTENT MAL'CEV CONDITIONS , 2011 .

[20]  R. Freese.  Equations implying congruence n-permutability and semidistributivity , 2013 .