THE ${\mathcal R}$- AND ${\mathcal L}$-ORDERS OF THE THOMPSON–HIGMAN MONOID Mk, 1 AND THEIR COMPLEXITY

2010 ◽  
Vol 20 (04) ◽  
pp. 489-524 ◽  
Author(s):  
JEAN-CAMILLE BIRGET
Keyword(s):  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Generating Set

We study the monoid generalization Mk, 1 of the Thompson–Higman groups, and we characterize the [Formula: see text]- and the [Formula: see text]-order of Mk, 1. Although Mk, 1 has only one nonzero [Formula: see text]-class and k-1 nonzero [Formula: see text]-classes, the [Formula: see text]- and the [Formula: see text]-order are complicated; in particular, [Formula: see text] is dense (even within an [Formula: see text]-class), and [Formula: see text] is dense (even within an [Formula: see text]-class). We study the computational complexity of the [Formula: see text]- and the [Formula: see text]-order. When inputs are given by words over a finite generating set of Mk, 1, the [Formula: see text]- and the [Formula: see text]-order decision problems are in P. However, over a "circuit-like" generating set the [Formula: see text]-order decision problem of Mk, 1 is [Formula: see text]-complete, whereas the [Formula: see text]-order decision problem is coNP-complete. Similarly, for acyclic circuits the surjectiveness problem is [Formula: see text]-complete, whereas the injectiveness problem is coNP-complete.

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.

scholarly journals Modal and mixed specifications: key decision problems and their complexities

2010 ◽  
Vol 20 (1) ◽  
pp. 75-103 ◽  
Author(s):  
ADAM ANTONIK ◽  
MICHAEL HUTH ◽  
KIM G. LARSEN ◽  
ULRIK NYMAN ◽  
ANDRZEJ WĄSOWSKI
Keyword(s):  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
List Type ◽  
Worst Case ◽  
Transition Systems ◽  
The Third ◽  
Mixed Transition

Modal and mixed transition systems are specification formalisms that allow the mixing of over- and under-approximation. We discuss three fundamental decision problems for such specifications: —whether a set of specifications has a common implementation;—whether an individual specification has an implementation; and—whether all implementations of an individual specification are implementations of another one. For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

scholarly journals COVID-19 Vaccination Priority Evaluation

2021 ◽  
Author(s):  
Jozo J Dujmovic ◽  
Daniel Tomasevich
Keyword(s):  
Decision Problem ◽  
Evaluation Method ◽  
Social Conditions ◽  
Decision Problems ◽  
Organ Transplants ◽  
Quantitative Criterion

Computing the COVID-19 vaccination priority is an urgent and ubiquitous decision problem. In this paper we propose a solution of this problem using the LSP evaluation method. Our goal is to develop a justifiable and explainable quantitative criterion for computing a vaccination priority degree for each individual in a population. Performing vaccination in the order of the decreasing vaccination priority produces maximum positive medical, social, and ethical effects for the whole population. The presented method can be expanded and refined using additional medical and social conditions. In addition, the same methodology is suitable for solving other similar medical priority decision problems, such as priorities for organ transplants.

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 Integrating imperfection of information into the promethee multicriteria decision aid methods: a general framework

2012 ◽  
Vol 37 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Sarah Ben Amor ◽  
Bertrand Mareschal
Keyword(s):  
Decision Problem ◽  
Decision Aid ◽  
General Framework ◽  
Imperfect Information ◽  
Possibility Theory ◽  
Decision Problems ◽  
Multicriteria Decision Aid ◽  
Multicriteria Decision ◽  
Information Models ◽  
Multicriteria Methods

Abstract.Multicriteria decision aid methods are used to analyze decision problems including a series of alternative decisions evaluated on several criteria. They most often assume that perfect information is available with respect to the evaluation of the alternative decisions. However, in practice, imprecision, uncertainty or indetermination are often present at least for some criteria. This is a limit of most multicriteria methods. In particular the PROMETHEE methods do not allow directly for taking into account this kind of imperfection of information. We show how a general framework can be adapted to PROMETHEE and can be used in order to integrate different imperfect information models such as a.o. probabilities, fuzzy logic or possibility theory. An important characteristic of the proposed approach is that it makes it possible to use different models for different criteria in the same decision problem.

Solving Decision Problems with Mathematical Expectation

2011 ◽  
Vol 128-129 ◽  
pp. 293-296
Author(s):  
Mei Zhang ◽  
Jing Hua Wen
Keyword(s):  
Mathematical Expectation ◽  
Decision Problem ◽  
Random Variables ◽  
Decision Problems ◽  
Employment Decision ◽  
Decision Variables ◽  
Project Contract

Mathematical expectation is one of the important digital characters of the random variables. Many decision variables in decision problem are random variables; it is difficult to define their concrete distribution, while we can use their mathematical expectation to resolve decision questions. The applications of mathematical expectation in decision question were analyzed by example from two aspects of project contract decision and obtain employment decision.

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.

Organizationally Intractable Decision Problems and the Intellectual Virtues of Heuristics

2017 ◽  
Vol 43 (8) ◽  
pp. 2620-2637 ◽  
Author(s):  
Richard A. Bettis
Keyword(s):  
Artificial Intelligence ◽  
Strategic Management ◽  
Decision Problem ◽  
Decision Problems ◽  
Allocation Decision ◽  
Mba Programs ◽  
Powerful Approach ◽  
Rules Of Thumb ◽  
Intractable Problems ◽  
Computational Intractability

There is no theory in strategic management and other related fields for identifying decision problems that cannot be solved by organizations using rational analytical technologies of the type typically taught in MBA programs. Furthermore, some and perhaps many scholars in strategic management believe that the alternative of heuristics or “rules of thumb” is little more than crude guesses for decision making when compared to rational analytical technologies. This is reflected in a paucity of research in strategic management on heuristics. I propose a theory of “organizational intractability” based roughly on the metaphor provided by “computational intractability” in computer science. I demonstrate organizational intractability for a common model of the joint strategic planning and resource allocation decision problem. This raises the possibility that heuristics are necessary for deciding many important decisions that are intractable for organizations. This possibility parallels the extensive use of heuristics in artificial intelligence for computationally intractable problems, where heuristics are often the most powerful approach possible. Some important managerial heuristics are documented from both the finance and strategic management literatures. Based on all of this, I discuss some directions for theory of and research on organizational intractability and heuristics in strategic management.

Prefix classes of Krom formulas

1973 ◽  
Vol 38 (4) ◽  
pp. 628-642 ◽  
Author(s):  
Stål O. Aanderaa ◽  
Harry R. Lewis
Keyword(s):  
Decision Problem ◽  
Decision Problems ◽  
Quantification Theory

In this paper we consider decision problems for subclasses of Kr, the class of those formulas of pure quantification theory whose matrices are conjunctions of binary disjunctions of signed atomic formulas. If each of Q1, …, Qn is an ∀ or an ∃, then let Q1 … Qn be the class of those closed prenex formulas with prefixes of the form (Q1x1)… (Qnxn). Our results may then be stated as follows:Theorem 1. The decision problem for satisfiability is solvable for the class ∀∃∀ ∩ Kr.Theorem 2. The classes ∀∃∀∀ ∩ Kr and ∀∀∃∀ ∩ Kr are reduction classes for satisfiability.Maslov [11] showed that the class ∃…∃∀…∀∃…∃ ∩ Kr is solvable, while the first author [1, Corollary 4] showed ∃∀∃∀ ∩ Kr and ∀∃∃∀ ∩ Kr to be reduction classes. Thus the only prefix subclass of Kr for which the decision problem remains open is ∀∃∀∃…∃∩ Kr.The class ∀∃∀ ∩ Kr, though solvable, contains formulas whose only models are infinite (e.g., (∀x)(∃u)(∀y)[(Pxy ∨ Pyx) ∧ (¬ Pxy ∨ ¬Pyu)], which can be satisfied over the integers by taking P to be ≥). This is not the case for Maslov's class ∃…∃∀…∀∃…∃ ∩ Kr, which contains no formula whose only models are infinite ([2] [5]).Theorem 1 was announced in [1, Theorem 4], but the proof sketched there is defective: Lemma 4 (p. 17) is incorrectly stated. Theorem 2 was announced in [9].

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