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SAT Solving
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem (SAT). On input a formula over Boolean data type, Boolean variables, such as "(''x'' or ''y'') and (''x'' or not ''y'')", a SAT solver outputs whether the formula is satisfiability, satisfiable, meaning that there are possible values of ''x'' and ''y'' which make the formula true, or unsatisfiable, meaning that there are no such values of ''x'' and ''y''. In this case, the formula is satisfiable when ''x'' is true, so the solver should return "satisfiable". Since the introduction of algorithms for SAT in the 1960s, modern SAT solvers have grown into complex software, software artifacts involving a large number of heuristics and program optimizations to work efficiently. By a result known as the Cook–Levin theorem, Boolean satisfiability is an NP-completeness, NP-complete problem in general. As a result, only algorithms with exponential worst-case comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to machine perception, perceive their environment and use machine learning, learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon (company), Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Amazon Alexa, Alexa); autonomous vehicles (e.g., Waymo); Generative artificial intelligence, generative and Computational creativity, creative tools (e.g., ChatGPT and AI art); and Superintelligence, superhuman play and analysis in strategy games (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OR-Tools
Google OR-Tools is a free and open-source software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related optimization problems. OR-Tools is a set of components written in C++ but provides wrappers for Java, .NET and Python. It is distributed under the Apache License 2.0. History OR-Tools was created by Laurent Perron in 2011. In 2014, Google's open source linear programming solver, GLOP, was released as part of OR-Tools. The CP-SAT solver bundled with OR-Tools has been consistently winning gold medals in the MiniZinc Challenge, an international constraint programming competition. Features The OR-Tools supports a variety of programming languages, including: * Object-oriented interfaces for C++ * A Java wrapper package * A .NET and .NET Framework wrapper package * A Python wrapper package OR-Tools supports a wide range of problem types, among them: * Ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GRASP (SAT Solver)
GRASP is a well known SAT The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and Test score, scoring have changed several times. For much of its history, it was called the Scholastic Aptitude Test ... instance solver. It was developed by João Marques Silva, a Portuguese computer science researcher. It stands for ''Generic seaRch Algorithm for the Satisfiability Problem''. External links GRASP home page References {{Reflist SAT solvers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaff Algorithm
Chaff is an algorithm for solving instances of the Boolean satisfiability problem in programming. It was designed by researchers at Princeton University. The algorithm is an instance of the DPLL algorithm with a number of enhancements for efficient implementation. Implementations Some available implementations of the algorithm in software are mChaff and zChaff, the latter one being the most widely known and used. zChaff was originally written by Dr. Lintao Zhang, at Microsoft Research, hence the “z”. It is now maintained by researchers at Princeton University and available for download as both source code and binaries on Linux Linux ( ) is a family of open source Unix-like operating systems based on the Linux kernel, an kernel (operating system), operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically package manager, pac .... zChaff is free for non-commercial use. References * M. Moskewicz, C. Madigan, Y. Zhao, L. Zhan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Propagation
Unit propagation (UP) or boolean constraint propagation (BCP) or the one-literal rule (OLR) is a procedure of automated theorem proving that can simplify a set of (usually propositional) clauses. Definition The procedure is based on unit clauses, i.e. clauses that are composed of a single literal, in conjunctive normal form. Because each clause needs to be satisfied, we know that this literal must be true. If a set of clauses contains the unit clause l, the other clauses are simplified by the application of the two following rules: # every clause (other than the unit clause itself) containing l is removed (the clause is satisfied if l is); # in every clause that contains \neg l this literal is deleted (\neg l can not contribute to it being satisfied). The application of these two rules lead to a new set of clauses that is equivalent to the old one. For example, the following set of clauses can be simplified by unit propagation because it contains the unit clause a. : \ Sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backjumping
In constraint programming and SAT solving, backjumping (also known as non-chronological backtracking or intelligent backtracking) is an enhancement for backtracking algorithms which reduces the search space. While backtracking always goes up one level in the search tree when all values for a variable have been tested, backjumping may go up more levels. In this article, a fixed order of evaluation of variables x_1,\ldots,x_n is used, but the same considerations apply to a dynamic order of evaluation. Image:Backtracking-no-backjumping.svg, A search tree visited by regular backtracking Image:Backtracking-with-backjumping.svg, A backjump: the grey node is not visited Definition Whenever backtracking has tried all values for a variable without finding any solution, it reconsiders the last of the previously assigned variables, changing its value or further backtracking if no other values are to be tried. If x_1=a_1,\ldots,x_k=a_k is the current partial assignment and all values for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications Of The ACM
''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with backgrounds in all areas of computer science and information systems. The focus is on the practical implications of advances in information technology and associated management issues; ACM also publishes a variety of more theoretical journals. The magazine straddles the boundary of a science magazine, trade magazine, and a scientific journal. While the content is subject to peer review, the articles published are often summaries of research that may also be published elsewhere. Material published must be accessible and relevant to a broad readership. From 1960 onward, ''CACM'' also published algorithms, expressed in ALGOL. The collection of algorithms later became known as the Collected Algorithms of the ACM. CA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conflict-driven Clause Learning
In computer science, conflict-driven clause learning (CDCL) is an algorithm for solving the Boolean satisfiability problem (SAT). Given a Boolean formula, the SAT problem asks for an assignment of variables so that the entire formula evaluates to true. The internal workings of CDCL SAT solvers were inspired by DPLL solvers. The main difference between CDCL and DPLL is that CDCL's backjumping is non-chronological. Conflict-driven clause learning was proposed by Marques-Silva and Karem A. Sakallah (1996, 1999) and Bayardo and Schrag (1997). Background Boolean satisfiability problem The satisfiability problem consists in finding a satisfying assignment for a given formula in conjunctive normal form (CNF). An example of such a formula is: :( ( not ''A'') or (not ''C'') ) and (''B'' or ''C''), or, using a common notation:In the pictures below, "+" is used to denote "or", multiplication to denote "and", and a postfix "'" to denote "not". :(\lnot A \lor \lnot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Davis–Putnam–Logemann–Loveland Algorithm
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem. It was introduced in 1961 by Martin Davis, George Logemann and Donald W. Loveland and is a refinement of the earlier Davis–Putnam algorithm, which is a resolution-based procedure developed by Davis and Hilary Putnam in 1960. Especially in older publications, the Davis–Logemann–Loveland algorithm is often referred to as the "Davis–Putnam method" or the "DP algorithm". Other common names that maintain the distinction are DLL and DPLL. Implementations and applications The SAT problem is important both from theoretical and practical points of view. In complexity theory it was the first problem proved to be NP-complete, and can appear in a broad variety of applications such as '' model checking'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Problem
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding whether a given natural number is prime. Another example is the problem, "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?" A decision procedure for a decision problem is an algorithmic method that answers the yes-no question on all inputs, and a decision problem is called decidable if there is a decision procedure for it. For example, the decision problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?" is decidable since there is a decision procedure called long division that gives the steps for determining whether ''x'' evenly divides ''y'' and the correct answer, ''YES'' or ''NO'', accordingly. Some of the most important problems in mathematics are undecidable, e.g. the halting problem. The field of computational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Logic Programming
Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is . In this clause, is a constraint; A(X,Y), B(X), and C(Y) are Literal (mathematical logic), literals as in regular logic programming. This clause states one condition under which the statement A(X,Y) holds: X+Y is greater than zero and both B(X) and C(Y) are true. As in regular logic programming, programs are queried about the provability of a goal, which itself may contain constraints in addition to literals. A proof for a goal is composed of clauses whose bodies are satisfiable constraints and literals that can in turn be proved using other clauses. Execution is performed by an interpreter, which starts from the goal and Recursion, recursively scans the clauses trying to prove the goa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
