No driver has ever made such an instant impact on the sport of F1 racing as Lewis Hamilton. The first black grand prix driver, his astonishing level of success in his rookie season together with his swash-buckling, attacking style has created a sensation. It has also been a central factor in the most exciting and controversial season of F1 in living memory as Hamilton was involved in a three-way fight for the world crown. Industrial espionage, claims of team favouritism and some stunning on-track action have peppered Hamilton's first season in the sport's top category. Here is the in-depth story of this phenomenon - from his upbringing on a Stevenage council estate to the day he first sat in a kart as a seven-year-old to his sensational challenge on the world title. Friends, colleagues, team-mates, rivals, chaperones and engineers who have worked with him here give some remarkable insights into Lewis the man and the driver, as well as into the close but complex relationship with father Anthony, the man who has largely steered his career. In the process, we see how F1 success has changed this young man's life in a very short space of time. "'Lewis Hamilton is on the verge of Tiger Woods-like status: forget his skin colour, it's about the emergence of a phenomenon. He's in the process of transcending the whole sport, imprinting himself into the consciousness of people who would normally have little or no interest in Formula One.' The Sunday Times, April 15, 2007" 1. Language: English. Narrator: Ben Elliot. Audio sample: http://samples.audible.de/bk/bbcw/003024/bk_bbcw_003024_sample.mp3. Digital audiobook in aax.
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.
High Quality Content by WIKIPEDIA articles! In computer science, the Satisfiability Modulo Theories (SMT) problem is a decision problem for logical formulas with respect to combinations of background theories expressed in classical first-order logic with equality. Examples of theories typically used in computer science are the theory of real numbers, the theory of integers, and the theories of various data structures such as lists, arrays, bit vectors and so on. Formally speaking, an SMT instance is a formula in first-order logic, where some function and predicate symbols have additional interpretations, and SMT is the problem of determining whether such a formula is satisfiable. In other words, imagine an instance of the Boolean satisfiability problem (SAT) in which some of the binary variables are replaced by predicates over a suitable set of non-binary variables. A predicate is basically a binary-valued function of non-binary variables. Example predicates include linear inequalities (e.g., 3x+ 2y - z geq 4) or equalities involving so-called uninterpreted terms and function symbols (e.g., f(f(u,v),v) = f(u,v) where f is some unspecified function of two unspecified arguments.)
High Quality Content by WIKIPEDIA articles! In computational complexity theory, a branch of computer science, Schaefer's theorem states necessary and sufficient conditions under which a finite set S of Boolean relations yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables. More precisely, Schaefer defines a decision problem which he calls the Generalized Satisfiability problem for S (denoted SAT(S)). The problem is to determine whether the given formula is satisfiable, in other words if the variables can be assigned values such that they satisfy all the constraints. Special cases of SAT(S) include the variants of Boolean satisfiability problem and the problem can also be viewed as a constraint satisfaction problem over the Boolean domain.
High Quality Content by WIKIPEDIA articles! The Valiant Vazirani theorem is an important result in computational complexity theory. It was proven by Leslie Valiant and Vijay Vazirani in their paper titled "NP is as easy as detecting unique solutions" published in 1986. The theorem states that if there is a polynomial time algorithm for UNIQUE-SAT, then NP=RP. The theorem implies that even if the number of satisfying assignments is very small, SAT (which is an NP-complete problem) still remains a hard problem. UNIQUE-SAT is a promise problem that decides whether a given Boolean formula is unsatisfiable or has exactly one satisfying assignment. In the first case a UNIQUE-SAT algorithm would reject, and in the second it would accept the formula. If the formula has more than one satisfying assignment then the behavior of the UNIQUE-SAT algorithm does not matter.
High Quality Content by WIKIPEDIA articles! The language TQBF is a formal language in computer science that contains True Quantified Boolean Formulas. A fully quantified boolean formula is a formula in first-order logic where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence. Any such formula is always either true or false (since there are no free variables). If such a formula evaluates to true, then that formula is in the language TQBF. It is also known as QSAT (Quantified SAT). In computational complexity theory, the quantified Boolean formula problem (QBF) is a generalization of the Boolean satisfiability problem in which both existential quantifiers and universal quantifiers can be applied to each variable.
This book provides a significant step towards bridging the areas of Boolean satisfiability and constraint satisfaction by answering the question why SAT-solvers are efficient on certain classes of CSP instances which are hard to solve for standard constraint solvers. The author also gives theoretical reasons for choosing a particular SAT encoding for several important classes of CSP instances.Boolean satisfiability and constraint satisfaction emerged independently as new fields of computer science, and different solving techniques have become standard for problem solving in the two areas. Even though any propositional formula (SAT) can be viewed as an instance of the general constraint satisfaction problem (CSP), the implications of this connection have only been studied in the last few years.The book will be useful for researchers and graduate students in artificial intelligence and theoretical computer science.
The satisfiability problem of propositional logic, SAT for short, is the first algorithmic problem that was shown to be NP-complete, and is the cornerstone of virtually all NP-completeness proofs. The SAT problem consists of deciding whether a given Boolean formula has a “solution”, in the sense of an assignment to the variables making the entire formula to evaluate to true.Over the last few years very powerful algorithms have been devised being able to solve SAT problems with hundreds of thousands of variables. For difficult (or randomly generated) formulas these algorithms can be compared to the proverbial search for the needle in a haystack. This book explains how such algorithms work, for example, by exploiting the structure of the SAT problem with an appropriate logical calculus, like resolution. But also algorithms based on “physical” principles are considered.
This book constitutes the refereed proceedings of the 19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016, held in Bordeaux, France, in July 2016.The 31 regular papers, 5 tool papers presented together with 3 invited talks were carefully reviewed and selected from 70 submissions. The papers address different aspects of SAT, including complexity, satisfiability solving, satisfiability applications, satisfiability modulop theory, beyond SAT, quantified Boolean formula, and dependency QBF.