Decision Procedures
Decision Procedures

Author: Daniel Kroening

Publisher: Springer Science & Business Media

Published: 2008-05-23

Total Pages: 314

ISBN-13: 3540741046

DOWNLOAD EBOOK

A decision procedure is an algorithm that, given a decision problem, terminates with a correct yes/no answer. Here, the authors focus on theories that are expressive enough to model real problems, but are still decidable. Specifically, the book concentrates on decision procedures for first-order theories that are commonly used in automated verification and reasoning, theorem-proving, compiler optimization and operations research. The techniques described in the book draw from fields such as graph theory and logic, and are routinely used in industry. The authors introduce the basic terminology of satisfiability modulo theories and then, in separate chapters, study decision procedures for each of the following theories: propositional logic; equalities and uninterpreted functions; linear arithmetic; bit vectors; arrays; pointer logic; and quantified formulas.

Multiple Decision Procedures
Multiple Decision Procedures

Author: Shanti S. Gupta

Publisher: SIAM

Published: 2002-01-01

Total Pages: 592

ISBN-13: 0898715326

DOWNLOAD EBOOK

An encyclopaedic coverage of the literature in the area of ranking and selection procedures. It also deals with the estimation of unknown ordered parameters. This book can serve as a text for a graduate topics course in ranking and selection. It is also a valuable reference for researchers and practitioners.

Multiple Objective Decision Making — Methods and Applications
Multiple Objective Decision Making — Methods and Applications

Author: C.-L. Hwang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 366

ISBN-13: 3642455115

DOWNLOAD EBOOK

Decision making is the process of selecting a possible course of action from all the available alternatives. In almost all such problems the multiplicity of criteria for judging the alternatives is pervasive. That is, for many such problems, the decision maker (OM) wants to attain more than one objective or goal in selecting the course of action while satisfying the constraints dictated by environment, processes, and resources. Another characteristic of these problems is that the objectives are apparently non commensurable. Mathematically, these problems can be represented as: (1. 1 ) subject to: gi(~) ~ 0, ,', . . . ,. ! where ~ is an n dimensional decision variable vector. The problem consists of n decision variables, m constraints and k objectives. Any or all of the functions may be nonlinear. In literature this problem is often referred to as a vector maximum problem (VMP). Traditionally there are two approaches for solving the VMP. One of them is to optimize one of the objectives while appending the other objectives to a constraint set so that the optimal solution would satisfy these objectives at least up to a predetermined level. The problem is given as: Max f. ~) 1 (1. 2) subject to: where at is any acceptable predetermined level for objective t. The other approach is to optimize a super-objective function created by multiplying each 2 objective function with a suitable weight and then by adding them together.

A Single-sample Multiple-decision Procedure for Selecting the Multinomial Event which Has the Highest Probability
A Single-sample Multiple-decision Procedure for Selecting the Multinomial Event which Has the Highest Probability

Author: Robert Eric Bechhofer

Publisher:

Published: 1957

Total Pages: 58

ISBN-13:

DOWNLOAD EBOOK

The problem of selecting the multinomial event which has the highest probability is formulated as a multiple-decision selection problem. Before experimentation starts the experimenter must specify two constants ([theta]*, P*) which are incorporated into the requirement: "The probability of a correct selection is to be equal to or greater than P* whenever the true (but unknown) ratio of the largest to the second largest of the poplation probabilities is equal to or greater than [theta]*." A single-sample procedure which meets the requirement is proposed. The heart of the procedure is the proper choice of N, the number of trials. Two methods of determining N are described: the first is exact and is to be used when N is small; the second is approximate and is to be used when N is large. Tables and sample calculations are provided.

A Sequential Multiple-decision Procedure for Selecting the Best One of Several Normal Populations with a Common Unknown Variance. Ii. Monte Carlo Sampling Results and New Computing Formulae
A Sequential Multiple-decision Procedure for Selecting the Best One of Several Normal Populations with a Common Unknown Variance. Ii. Monte Carlo Sampling Results and New Computing Formulae

Author: Robert Eric Bechhofer

Publisher:

Published: 1961

Total Pages: 62

ISBN-13:

DOWNLOAD EBOOK

Contents: Statement of the statistical problem S atistical assumptions The experimenter's goal, specification, and requirement Procedure D and the new computing formulae Description of Procedure D Definition of symbols The sampling, stopping, and terminal de cision rules Computation of the stopping statistic Use of Procedure D (method B) with various experimental designs Simplified computing formulae Numerical example Monte Carlo sampling results with Procedure D Description of the sampling procedure Sampling results Discussion of sampling results.

Evaluation and Decision Models with Multiple Criteria
Evaluation and Decision Models with Multiple Criteria

Author: Denis Bouyssou

Publisher: Springer Science & Business Media

Published: 2006-06-07

Total Pages: 460

ISBN-13: 0387310991

DOWNLOAD EBOOK

Formal decision and evaluation models are so widespread that almost no one can pretend not to have used or suffered the consequences of one of them. This book is a guide aimed at helping the analyst to choose a model and use it consistently. A sound analysis of techniques is proposed and the presentation can be extended to most decision and evaluation models as a "decision aiding methodology".