Erscheinungsdatum: 07.02.2019, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Zhegalkin Polynomial SAT Solver, Titelzusatz: Zhegalkin SAT Solver (ZPSAT) is a efficient alternative to solve Boolean functions systems, Autor: Fernandez Davila, Jorge, Verlag: EAE, Sprache: Englisch, Rubrik: Informatik // EDV, Sonstiges, Seiten: 52, Informationen: Paperback, Gewicht: 98 gr, Verkäufer: averdo
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Polynomial systems are fundamental tools in the solution of hard problems in science and engineering such as robotics, automated reasoning, artificial intelligence and signal processing. Similarly, from the early days of the digital era, Boolean variables have been the foundations of the computer operations. Hence, the application of common algebraic techniques to Boolean algebra is used now as a method to solve complex Boolean equation systems that before were only intended to solve using Boolean logic techniques. The aim of this project is to demonstrate that Zhegalkin polynomials (also known as Algebraic Normal Form - ANF) are an alternative way to represent Boolean functions. In order to test the hypothesis, a Zhegalkin SAT Solver (ZPSAT) was developed. The results conducted after the testing concluded that ZPSAT can solve a conjunction of XOR equations efficiently in terms of reliability and computing time. The heuristic used to build ZPSAT was based mainly on the concepts used by the Horn Formulae and a Fast-Multiplication method of two ANF polynomials known as Mobius transform.
NP Complete (abbreviated as NPC) problems, standing at the crux of deciding whether P=NP, are among hardest problems in computer science and other related areas. Observing that NPC problems have different natures, they can be further classified. We show that the classification of NPC problems may depend on their natures, reduction methods, exact algorithms, and the boundary between P and NP. We propose a new perspective: both P problems and NPC problems have the duality feature in terms of computational complexity of asymptotic efficiency of algorithms. We then introduce near optimal solutions to some NPC problems such as Traveling Salesman Problems (TSP), Boolean Satisfiability Problems (SAT), Scheduling algorithms in Cloud data centers and Bigdata process platforms. These solutions may shine light on other NPC problems and their applications.
The TM-LPSAT planner can construct plans in domains containing atomic actions and durative actions, events and processes, discrete, real-valued, and interval-valued fluents, reusable resources,both numeric and interval-valued, and continuous linear change to quantities. It works in three tages.In the first stage, a representation of the domain and problem in an extended version of PDDL+ iscompiled into a system of Boolean combinations of propositional atoms and linear constraints overnumeric variables. In the second stage, a SAT-based arithmetic constraint solver, such as LPSAT orMathSAT, is used to find a solution to the system of constraints. In the third stage, a correct plan isextracted from this solution. We discuss the structure of the planner and show how planning withtime and metric quantities is compiled into a system of constraints.
Revision with unchanged content. Automatic program analysis tools are increasingly developed and deployed to combat the perenniel software quaility problem that plagues the IT industry. Traditional tools faces a stark tradeoff between precision and scalability: scalable tools are often imprecise, limiting themselves to detecting relatively shallow errors, precise tools are often not scalable and are thus only applied to simplified models of the core parts of large systems. This study presents techniques and results on how to exploit existing struc tures of large software systems to make precise program analyses scale. As an example, the author show how to scale Boolean Satisfiability (SAT) based a na lysis - traditionally applied to small models with hundreds of lines of code - to the whole Linux kernel, which contains millions of lines of code. This study is directed to designers and users of software analysis tools alike. It offers detailed descriptions of several state-of-the-art automatic error detection algorithms and presents experimental results on mature open-source systems. The approach can be potentially generalized to the design and deployment of a wide range of program analysis tools.
The Boolean conjunctive normal form (CNF) satisability problem, called SAT for short, gets as input a CNF formula and has to decide whether this formula admits a satisfying truth assignment. As is well known, the remarkable result by S. Cook in 1971 established SAT as the first and genuine complete problem for the complexity class NP. In this thesis we consider SAT for a subclass of CNF, the so called Mixed Horn formula class (MHF). A formula F 2 MHF consists of a 2-CNF part P and a Horn part H. We propose that MHF has a central relevance in CNF because many prominent NP-complete problems, e.g. Feedback Vertex Set, Vertex Cover, Dominating Set and Hitting Set, can easily be encoded as MHF. Furthermore, we show that SAT remains NP-complete for some interesting subclasses of MHF. We also provide algorithms for some of these subclasses solving SAT in a better running time than O(2^0.5284n) which is the best bound for MHF so far. In addition, we investigate the computational complexity of some prominent variants of SAT, namely not-all-equal SAT (NAE-SAT) and exact SAT (XSAT) restricted to the class of linear CNF formulas.
There are many complex problems in computer science that occur in knowledge-representation, artificial learning, Very Large Scale Integration (VLSI) design, security protocols and other areas. These complex problems may be deduced into satisfiability problems where the Boolean Satisfiability Problem (SAT) may be applied. This deduction is made in order to simplify complex problems into a specific propositional logic problem. The SAT problem is the most well-known nondeterministic polynomial time (NP) complete problem in computer science. In this book, we solve the SAT problem using a clustering technique - Multilevel - combined first with the Tabu Search algorithm and combined thereafter with finite Learning Automata. Tabu Search and finite Learning Automata are two very efficient approaches that have been used to solve SAT.