scholarly journals Polynomial-time tests for difference terms in idempotent varieties

2019 ◽  
Vol 29 (06) ◽  
pp. 927-949
Author(s):  
William DeMeo ◽  
Ralph Freese ◽  
Matthew Valeriote

We consider the following practical question: given a finite algebra [Formula: see text] in a finite language, can we efficiently decide whether the variety generated by [Formula: see text] has a difference term? We answer this question (positively) in the idempotent case and then describe algorithms for constructing difference term operations.

2000 ◽  
Vol 65 (1) ◽  
pp. 187-200 ◽  
Author(s):  
Ross Willard

AbstractWe derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given m < ω and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.


2009 ◽  
Vol 19 (01) ◽  
pp. 41-77 ◽  
Author(s):  
RALPH FREESE ◽  
MATTHEW A. VALERIOTE

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.


2004 ◽  
Vol 14 (03) ◽  
pp. 325-355
Author(s):  
ROSS WILLARD

Using techniques pioneered by R. McKenzie, we prove that there is no algorithm which, given a finite algebra in a finite language, determines whether the variety (equational class) generated by the algebra has a model companion. In particular, there exists a finite algebra such that the variety it generates has no model companion; this answers a question of Burris and Werner from 1979.


2006 ◽  
Vol 16 (03) ◽  
pp. 563-581 ◽  
Author(s):  
BENOIT LAROSE ◽  
LÁSZLÓ ZÁDORI

We study the algorithmic complexity of determining whether a system of polynomial equations over a finite algebra admits a solution. We characterize, within various families of algebras, which of them give rise to an NP-complete problem and which yield a problem solvable in polynomial time. In particular, we prove a dichotomy result which encompasses the cases of lattices, rings, modules, quasigroups and also generalizes a result of Goldmann and Russell for groups [15].


2010 ◽  
Vol 20 (08) ◽  
pp. 1001-1020 ◽  
Author(s):  
TOMASZ A. GORAZD ◽  
JACEK KRZACZKOWSKI

We study the computational complexity of the satisfiability problem of an equation between terms over a finite algebra (TERM-SAT). We describe many classes of algebras where the complexity of TERM-SAT is determined by the clone of term operations. We classify the complexity for algebras generating maximal clones. Using this classification we describe many of algebras where TERM-SAT is NP-complete. We classify the situation for clones which are generated by an order or a permutation relation. We introduce the concept of semiaffine algebras and show polynomial-time algorithms which solve the satisfiability problem for them.


2018 ◽  
Vol 60 (2) ◽  
pp. 360-375
Author(s):  
A. V. Vasil'ev ◽  
D. V. Churikov

Author(s):  
Oren Izenberg

This book offers a new way to understand the divisions that organize twentieth-century poetry. It argues that the most important conflict is not between styles or aesthetic politics, but between poets who seek to preserve or produce the incommensurable particularity of experience by making powerful objects, and poets whose radical commitment to abstract personhood seems altogether incompatible with experience—and with poems. Reading across the apparent gulf that separates traditional and avant-garde poets, the book reveals the common philosophical urgency that lies behind diverse forms of poetic difficulty—from William Butler Yeats's esoteric symbolism and George Oppen's minimalism and silence to Frank O'Hara's joyful slightness and the Language poets' rejection of traditional aesthetic satisfactions. For these poets, what begins as a practical question about the conduct of literary life—what distinguishes a poet or group of poets?—ends up as an ontological inquiry about social life: What is a person and how is a community possible? In the face of the violence and dislocation of the twentieth century, these poets resist their will to mastery, shy away from the sensual richness of their strongest work, and undermine the particularity of their imaginative and moral visions—all in an effort to allow personhood itself to emerge as an undeniable fact making an unrefusable claim.


10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.


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