scholarly journals Deciding the Existence of Minority Terms

2019 ◽  
Vol 63 (3) ◽  
pp. 577-591
Author(s):  
Alexandr Kazda ◽  
Jakub Opršal ◽  
Matt Valeriote ◽  
Dmitriy Zhuk
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Decision Problem ◽  
Idempotent Algebra ◽  
Term Operation

AbstractThis paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation $m$ that satisfies the minority equations $m(y,x,x)\approx m(x,y,x)\approx m(x,x,y)\approx y$. 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.

scholarly journals EXACT NON-IDENTITY CHECK IS NQP-COMPLETE

2010 ◽  
Vol 08 (05) ◽  
pp. 807-819
Author(s):  
YU TANAKA
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Decision Problem ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Unitary Operation ◽  
Classical Description ◽  
Quantum Polynomial ◽  
Equivalence Check

To understand quantum gate array complexity, we define a problem named exact non-identity check, which is a decision problem to determine whether a given classical description of a quantum circuit is strictly equivalent to the identity or not. We show that the computational complexity of this problem is non-deterministic quantum polynomial-time (NQP)-complete. As corollaries, it is derived that exact non-equivalence check of two given classical descriptions of quantum circuits is also NQP-complete and that minimizing the number of quantum gates for a given quantum circuit without changing the implemented unitary operation is NQP-hard.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

COMPUTATIONAL COMPLEXITY OF VARIOUS MAL'CEV CONDITIONS

2013 ◽  
Vol 23 (06) ◽  
pp. 1521-1531 ◽  
Author(s):  
JONAH HOROWITZ
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Mal’Cev Condition ◽  
Exponential Time ◽  
Cube Term ◽  
Near Unanimity

This paper examines the computational complexity of determining whether or not an algebra satisfies a certain Mal'Cev condition. First, we define a class of Mal'Cev conditions whose satisfaction can be determined in polynomial time (special cube term satisfying the DCP) when the algebra in question is idempotent and provide an algorithm through which this determination may be made. The aforementioned class notably includes near unanimity terms and edge terms of fixed arity. Second, we define a different class of Mal'Cev conditions whose satisfaction, in general, requires exponential time to determine (Mal'Cev conditions satisfiable by CPB0 operations).

scholarly journals IT IS NL-COMPLETE TO DECIDE WHETHER A HAIRPIN COMPLETION OF REGULAR LANGUAGES IS REGULAR

2011 ◽  
Vol 22 (08) ◽  
pp. 1813-1828 ◽  
Author(s):  
VOLKER DIEKERT ◽  
STEFFEN KOPECKI
Keyword(s):  
Polynomial Time ◽  
Dna Computing ◽  
Regular Language ◽  
Decision Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Complexity Bound ◽  
The One ◽  
Context Free ◽  
Hairpin Formation

The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular language is linear context-free, but not regular, in general. However, for some time it is was open whether the regularity of the hairpin completion of a regular language is decidable. In 2009 this decidability problem has been solved positively in [5] by providing a polynomial time algorithm. In this paper we improve the complexity bound by showing that the decision problem is actually NL-complete. This complexity bound holds for both, the one-sided and the two-sided hairpin completions.

MODEL NET: A REPRESENTATION OF THE STATIC STRUCTURE OF MODELBASE

2007 ◽  
Vol 21 (04) ◽  
pp. 791-807 ◽  
Author(s):  
CHANGSONG QI ◽  
JIGUI SUN
Keyword(s):  
Computational Complexity ◽  
Directed Graph ◽  
Decision Problem ◽  
Formal Definition ◽  
Model Composition ◽  
Static Structure ◽  
Construction Algorithm ◽  
Composite Models ◽  
Definition Of

Model net proposed in this paper is a kind of directed graph used to represent and analyze the static structure of a modelbase. After the formal definition of the model net was given, a construction algorithm is introduced. Then, two simplification algorithms are put forward to show how this approach can reduce the computational complexity of model composition for a specific decision problem. In succession, a model composition algorithm is worked out based on the simplification algorithms. As a result, this algorithm is capable of finding out all the candidate composite models for a specific decision problem. Finally, several advantages of the model net are discussed briefly.

scholarly journals Computational Complexity of Topological Invariants

2014 ◽  
Vol 58 (1) ◽  
pp. 27-32
Author(s):  
Manuel Amann
Keyword(s):  
Computational Complexity ◽  
Decision Problem ◽  
Topological Invariants ◽  
Np Hard ◽  
Connected Space ◽  
Finite Dimensional ◽  
Lusternik Schnirelmann ◽  
Simply Connected

AbstractWe answer the following question posed by Lechuga: given a simply connected spaceXwith bothH*(X; ℚ) and π*(X) ⊗ ℚ being finite dimensional, what is the computational complexity of an algorithm computing the cup length and the rational Lusternik—Schnirelmann category ofX?Basically, by a reduction from the decision problem of whether a given graph isk-colourable fork≥ 3, we show that even stricter versions of the problems above are NP-hard.

scholarly journals The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Linqiang Pan ◽  
Bosheng Song ◽  
Luis Valencia-Cabrera ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Computational Complexity ◽  
Natural Number ◽  
Polynomial Time ◽  
Cell Separation ◽  
Computational Models ◽  
P Systems ◽  
Fission Process ◽  
Work Cell ◽  
Membrane Fission ◽  
Biochemical Systems

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules. The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (n,1), for each natural number n≥1. In the case where that length is upper bounded by (3,2), a polynomial time solution to the SAT problem is provided, hence, assuming that P≠NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem.

The Complexity of Deciding Strictly Non-Blocking Concentration and Generalized-Concentration Properties

1997 ◽  
Vol 08 (03) ◽  
pp. 237-252 ◽  
Author(s):  
H. K. Dai
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Strict Sense ◽  
Small Depth ◽  
Directed Paths ◽  
Concentration Properties ◽  
Vertex Disjoint ◽  
Matching Techniques

Concentrators and generalized-concentrators are interconnection networks that provide respectively pairwise vertex-disjoint directed paths and trees to satisfy interconnection requests. An interconnection network is non-blocking in the strict sense if every compatible interconnection request can be satisfied by a path regardless of any existing interconnections. We present polynomial time computational complexity results for deciding the strictly non-blocking concentration and generalized-concentration properties with small depth, by using b-matching techniques.

Sign in / Sign up

Export Citation Format

Share Document