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121 relations: Algorithm, Algorithmics, Approximation algorithm, APX, Artificial intelligence, ASCII, Automated planning and scheduling, Automated theorem proving, Automatic test pattern generation, Backjumping, Binary decision diagram, Boolean algebra, Boolean algebra (structure), Boolean ring, BPP (complexity), Chaff algorithm, Circuit design, Circuit satisfiability problem, Clique problem, Co-NP-complete, Communications of the ACM, Complexity class, Computational complexity theory, Computer science, Conflict-Driven Clause Learning, Conjunctive normal form, Constraint satisfaction problem, Cook–Levin theorem, Cryptography, David S. Johnson, Decision problem, Disjunctive normal form, DPLL algorithm, Electronic design automation, Equisatisfiability, Exclusive or, Existential quantification, Exponential time hypothesis, Field-programmable gate array, Finite field, First-order logic, FNP (complexity), Formal equivalence checking, Formal verification, FP (complexity), Free and open-source software, Gaussian elimination, Genetic algorithm, Graph (discrete mathematics), GRASP (SAT solver), ..., Horn clause, Interpretation (logic), Karloff–Zwick algorithm, Karp's 21 NP-complete problems, Karp–Lipton theorem, L (complexity), Leonid Levin, Linear programming, Local search (constraint satisfaction), Logical conjunction, Logical consequence, Logical disjunction, Logical equivalence, Maximum satisfiability problem, Michael Garey, Microprocessor, Model checking, Negation, NL (complexity), NL-complete, NP (complexity), NP-completeness, NP-hardness, P (complexity), P system, P versus NP problem, P-complete, P/poly, PH (complexity), Polynomial-time approximation scheme, Polynomial-time reduction, PP (complexity), Processor design, Promise problem, Propositional calculus, PSPACE-complete, Quantifier (logic), Reduction (complexity), Resolution (logic), Routing (electronic design automation), RP (complexity), Satisfiability, Satisfiability modulo theories, Schaefer's dichotomy theorem, Scheduling (computing), Second-order logic, Sharp-P-complete, Sharp-SAT, SL (complexity), Stephen Cook, Stochastic, Substitution (logic), Symposium on Theory of Computing, Tautology (logic), Theoretical computer science, Thomas Jerome Schaefer, Time complexity, True quantified Boolean formula, Truth value, Turing machine, Uninterpreted function, Unit propagation, Universal quantification, University of Toronto, Unsatisfiable core, Valiant–Vazirani theorem, Validity, Variable (mathematics), WalkSAT, Well-formed formula, 2-satisfiability. Expand index (71 more) »
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Algorithmics
Algorithmics is the science of algorithms.
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Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
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APX
In complexity theory the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short).
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Artificial intelligence
Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.
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ASCII
ASCII, abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication.
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Automated planning and scheduling
Automated planning and scheduling, sometimes denoted as simply AI Planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles.
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Automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs.
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Automatic test pattern generation
ATPG (acronym for both Automatic Test Pattern Generation and Automatic Test Pattern Generator) is an electronic design automation method/technology used to find an input (or test) sequence that, when applied to a digital circuit, enables automatic test equipment to distinguish between the correct circuit behavior and the faulty circuit behavior caused by defects.
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Backjumping
In backtracking algorithms, backjumping is a technique that reduces search space, therefore increasing efficiency.
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Binary decision diagram
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.
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Boolean ring
In mathematics, a Boolean ring R is a ring for which x2.
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BPP (complexity)
In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded away from 1/2 for all instances.
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Chaff algorithm
Chaff is an algorithm for solving instances of the Boolean satisfiability problem in programming.
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Circuit design
The process of circuit design can cover systems ranging from complex electronic systems all the way down to the individual transistors within an integrated circuit.
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Circuit satisfiability problem
In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true.
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Clique problem
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.
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Co-NP-complete
In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP-complete problem with only polynomial overhead.
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Communications of the ACM
Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Conflict-Driven Clause Learning
In computer science, conflict-driven clause learning (CDCL) is an algorithm for solving the Boolean satisfiability problem (SAT).
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Conjunctive normal form
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is an AND of ORs.
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Constraint satisfaction problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.
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Cook–Levin theorem
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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David S. Johnson
David Stifler Johnson (December 9, 1945 – March 8, 2016) was an American computer scientist specializing in algorithms and optimization.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Disjunctive normal form
In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept.
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DPLL algorithm
In 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.
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Electronic design automation
Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards.
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Equisatisfiability
In logic, two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or both are not.
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Exclusive or
Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).
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Existential quantification
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
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Exponential time hypothesis
In computational complexity theory, the exponential time hypothesis is an unproven computational hardness assumption that was formulated by.
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Field-programmable gate array
A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturing hence "field-programmable".
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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FNP (complexity)
In computational complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP.
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Formal equivalence checking
Formal equivalence checking process is a part of electronic design automation (EDA), commonly used during the development of digital integrated circuits, to formally prove that two representations of a circuit design exhibit exactly the same behavior.
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Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.
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FP (complexity)
In computational complexity theory, the complexity class FP is the set of function problems which can be solved by a deterministic Turing machine in polynomial time; it is the function problem version of the decision problem class P. Roughly speaking, it is the class of functions that can be efficiently computed on classical computers without randomization.
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Free and open-source software
Free and open-source software (FOSS) is software that can be classified as both free software and open-source software.
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Gaussian elimination
In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
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Genetic algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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GRASP (SAT solver)
GRASP is a well known SAT instance solver.
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Horn clause
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form which gives it useful properties for use in logic programming, formal specification, and model theory.
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Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language.
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Karloff–Zwick algorithm
The Karloff–Zwick algorithm, in computational complexity theory, is a randomised approximation algorithm taking an instance of MAX-3SAT Boolean satisfiability problem as input.
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Karp's 21 NP-complete problems
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.
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Karp–Lipton theorem
In complexity theory, the Karp–Lipton theorem states that if the Boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial number of logic gates, then That is, if we assume that NP, the class of nondeterministic polynomial time problems, can be contained in the non-uniform polynomial time complexity class P/poly, then this assumption implies the collapse of the polynomial hierarchy at its second level.
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L (complexity)
In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space.
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Leonid Levin
Leonid Anatolievich Levin (Леони́д Анато́льевич Ле́вин; Леоні́д Анато́лійович Ле́він; born November 2, 1948) is a Soviet-American computer scientist.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Local search (constraint satisfaction)
In constraint satisfaction, local search is an incomplete method for finding a solution to a problem.
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Logical conjunction
In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.
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Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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Logical disjunction
In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.
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Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.
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Maximum satisfiability problem
In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula.
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Michael Garey
Michael Randolph Garey is a computer science researcher, and co-author (with David S. Johnson) of Computers and Intractability: A Guide to the Theory of NP-completeness.
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Microprocessor
A microprocessor is a computer processor that incorporates the functions of a central processing unit on a single integrated circuit (IC), or at most a few integrated circuits.
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Model checking
In computer science, model checking or property checking refers to the following problem: Given a model of a system, exhaustively and automatically check whether this model meets a given specification.
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Negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.
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NL (complexity)
In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems which can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.
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NL-complete
In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.
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NP (complexity)
In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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NP-hardness
NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".
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P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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P system
A P system is a computational model in the field of computer science that performs calculations using a biologically-inspired process.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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P-complete
In complexity theory, a decision problem is P-complete (complete for the complexity class '''P''') if it is in P and every problem in P can be reduced to it by an appropriate reduction.
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P/poly
In computational complexity theory, P/poly is the complexity class of languages recognized by a polynomial-time Turing machine with a polynomial-bounded advice function.
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PH (complexity)
In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy: PH was first defined by Larry Stockmeyer.
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Polynomial-time approximation scheme
In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).
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Polynomial-time reduction
In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.
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PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances.
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Processor design
Processor design is the design engineering task of creating a processor, a component of computer hardware.
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Promise problem
In computational complexity theory, a promise problem is a generalization of a decision problem where the input is promised to belong to a particular subset of all possible inputs.
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Propositional calculus
Propositional calculus is a branch of logic.
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PSPACE-complete
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.
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Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
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Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.
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Resolution (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic.
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Routing (electronic design automation)
In electronic design, wire routing, commonly called simply routing, is a step in the design of printed circuit boards (PCBs) and integrated circuits (ICs).
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RP (complexity)
In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics.
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Satisfiability modulo theories
In computer science and mathematical logic, 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.
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Schaefer's dichotomy theorem
In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables.
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Scheduling (computing)
In computing, scheduling is the method by which work specified by some means is assigned to resources that complete the work.
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Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.
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Sharp-P-complete
#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory.
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Sharp-SAT
In computational complexity theory, #SAT, or Sharp-SAT, a function problem related to the Boolean satisfiability problem, is the problem of counting the number of satisfying assignments of a given Boolean formula.
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SL (complexity)
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component.
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Stephen Cook
Stephen Arthur Cook, (born December 14, 1939) is an American-Canadian computer scientist and mathematician who has made major contributions to the fields of complexity theory and proof complexity.
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Stochastic
The word stochastic is an adjective in English that describes something that was randomly determined.
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Substitution (logic)
Substitution is a fundamental concept in logic.
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Symposium on Theory of Computing
The Annual ACM Symposium on Theory of Computing (STOC) is an academic conference in the field of theoretical computer science.
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Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
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Theoretical computer science
Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
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Thomas Jerome Schaefer
Thomas Jerome Schaefer is an American mathematician.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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True quantified Boolean formula
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.
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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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Turing machine
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.
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Uninterpreted function
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and n-ary form.
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Unit propagation
Unit propagation (UP) or Boolean Constraint propagation or the one-literal rule (OLR) is a procedure of automated theorem proving that can simplify a set of (usually propositional) clauses.
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Universal quantification
In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".
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University of Toronto
The University of Toronto (U of T, UToronto, or Toronto) is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen's Park.
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Unsatisfiable core
In mathematical logic, given an unsatisfiable Boolean propositional formula in conjunctive normal form, a subset of clauses whose conjunction is still unsatisfiable is called an unsatisfiable core of the original formula.
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Valiant–Vazirani theorem
The Valiant–Vazirani theorem is a theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT, then NP.
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Validity
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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WalkSAT
In computer science, GSAT and WalkSAT are local search algorithms to solve Boolean satisfiability problems.
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Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
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2-satisfiability
In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables.
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References
[1] https://en.wikipedia.org/wiki/Boolean_satisfiability_problem
