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.

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.

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.

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.

Skepticism, reason, and decision

2018 ◽  
Author(s):  
◽  
Tung-Ying Wu
Keyword(s):  
Decision Theory ◽  
Decision Problem ◽  
Ethical Theory ◽  
Ideal Observer ◽  
University Of Missouri ◽  
The Third ◽  
History Of ◽  
The University ◽  
The Ideal

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] "This dissertation is a combination of three different projects. The first project investigates the history of philosophy: Kant's refutation of idealism. In this project I propose a more plausible interpretation of Kant's argument against idealism. Next, the second project investigates ethical theory: the ideal observer view. There, I criticize an argument for ideal observer view as untenable. Finally, the third project investigates decision theory: the decision problem: Psycho Buttons. I argue that causal decision theory supplemented with Full Information does not lead to intransitivity in Psycho Buttons. In this chapter I present an introduction to each project." --Introduction

scholarly journals On a Propositional Calculus Whose Decision Problem is Recursively Unsolvable

1970 ◽  
Vol 38 ◽  
pp. 145-152
Author(s):  
Akira Nakamura
Keyword(s):  
Decision Problem ◽  
Propositional Calculus ◽  
Predicate Calculus ◽  
Reduction Theorem ◽  
List Type ◽  
First Order ◽  
Order Predicate Calculus

The purpose of this paper is to present a propositional calculus whose decision problem is recursively unsolvable. The paper is based on the following ideas: (1) Using Löwenheim-Skolem’s Theorem and Surányi’s Reduction Theorem, we will construct an infinitely many-valued propositional calculus corresponding to the first-order predicate calculus.(2) It is well known that the decision problem of the first-order predicate calculus is recursively unsolvable.(3) Thus it will be shown that the decision problem of the infinitely many-valued propositional calculus is recursively unsolvable.

WORST-CASE SCENARIOS FOR AMERICAN OPTIONS

2000 ◽  
Vol 03 (01) ◽  
pp. 25-58
Author(s):  
ROBERT BUFF
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
American Options ◽  
Worst Case ◽  
Knock Out ◽  
Early Exercise ◽  
Pricing Options ◽  
Diffusion Parameters ◽  
Volatility Models ◽  
Compute Time

One approach to cope with uncertain diffusion parameters when pricing options portfolios is to identify the parameters [Formula: see text] in a subset [Formula: see text] of the parameter space which form the worst-case for a particular portfolio. For the sell-side, this leads to a nonlinear algorithm that maximizes the expected liability under the risk-neutral measure. [Formula: see text] depends on the portfolio under consideration. Moreover, the algorithm must take into account that the exposure to [Formula: see text]-risk changes when non-vanilla components such as barrier or American options knock out or are exercised early. In this paper, we describe techniques to price portfolios with American options under worst-case scenarios based on uncertain volatility models. We also present heuristics which reduce the computational complexity that arises from the necessity to consider many early exercise combinations at a time. These heuristics reduce the compute time by almost one half.

scholarly journals Part 2: The Third International Radiocarbon Intercomparison (Tiri)

Radiocarbon ◽  
2003 ◽  
Vol 45 (2) ◽  
pp. 293-328 ◽  
Keyword(s):  
Quality Assurance ◽  
Objective Measure ◽  
List Type ◽  
Type Number ◽  
Analytical Quality ◽  
The Third ◽  
Self Help ◽  
The World

TIRI was officially launched at the 14th International Radiocarbon Conference in Arizona in 1991. Prior to the conference, 150 laboratories received a letter describing the general intention to organize an intercomparison and over 90 laboratories from around the world responded positively to the invitation to participate. Simply stated, the aims of this intercomparison were: 1.To function as the third arm of the quality assurance (QA) procedure.2.To provide an objective measure of the maintenance and improvement in analytical quality.3.To assist in the development of a “self-help” scheme for participating laboratories.

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.

Some New Methods of Precision X-Ray Spectrometry

1972 ◽  
Vol 16 ◽  
pp. 251-259 ◽  
Author(s):  
K. Das Gupta ◽  
Herbert Welch ◽  
P.F. Gott ◽  
John F. Priest ◽  
Sunny Cheng ◽  
...  
Keyword(s):  
Focal Point ◽  
Spectral Lines ◽  
Background Intensity ◽  
List Type ◽  
Crystal Spectrometer ◽  
X Ray ◽  
Bent Crystal ◽  
The Third ◽  
Light Gathering Power ◽  
In Series

AbstractThree novel methods of x-ray spectrometry have been developed in recent years at Texas Tech University. These are:1. Three crystal spectrometer2. Two curved crystal spectrometer3. Spherically bent crystal spectrometer.In this paper the new design features, and experimental results will be discussed to indicate the usefulness of the new instruments. The three crystal spectrometer is a modified two crystal instrument. A third crystal is used to analyze the output of the two crystal spectrometer. The first two crystals are operated as a standard two crystal spectrometer. The third crystal is swept through the spectrum transmitted by the first two crystals for each setting of the first two crystals. The peak intensity of the third crystal sweep corresponds to the energy setting of the two crystal spectrometer, and is the intensity used to plot the spectral lines. The two curved crystal spectrometer utilizes two transmission spectrographs with radii having a 2:1 ratio in series, the crystal with the smaller radius being set so that its focal point falls on the Rowland circle of the larger radius crystal, This instrument has a very low background intensity and is suitable for precision scattering and diffraetion work. The spherically bent crystal spectrometer makes use of high light gathering power and high orders of reflection to allow high resolution studies of weak spectral lines. It also has the advantage of ease of alignment and operation.

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