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Classic NP-complete problem in computer science
computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether
Circuit satisfiability problem
Circuit_satisfiability_problem
Problem of determining if a Boolean formula could be made true
science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) asks whether
Boolean satisfiability problem
Boolean_satisfiability_problem
Logic problem, AND of pairwise ORs
more general problems, which are NP-complete, 2-satisfiability can be solved in polynomial time. Instances of the 2-satisfiability problem are typically
2-satisfiability
Existence of values making formula true
Bockmayr and Weispfenning. 2-satisfiability Boolean satisfiability problem Circuit satisfiability Karp's 21 NP-complete problems Validity Constraint satisfaction
Satisfiability
Computational problem
which is complete for co-NP. Circuit satisfiability Switching lemma Samuel R. Buss (Jan 1987). "The Boolean formula value problem is in ALOGTIME". In Alfred
Circuit_value_problem
other NP-completeness results. Circuit satisfiability problem Conjunctive Boolean query Cyclic ordering Exact cover problem. Remains NP-complete for 3-sets
List_of_NP-complete_problems
Set of computational problems stated by Richard Karp (1973)
NP-complete by reducing Exact cover to Knapsack. Satisfiability: the Boolean satisfiability problem for formulas in conjunctive normal form (often referred
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Logical problem studied in computer science
mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the
Satisfiability modulo theories
Satisfiability_modulo_theories
Task of computing complete subgraphs
sequence of bits. An instance of the satisfiability problem should have a valid proof if and only if it is satisfiable. The proof is checked by an algorithm
Clique_problem
Unsolved problem in computer science
Theory and Applications of Satisfiability Testing – SAT 2007. International Conference on Theory and Applications of Satisfiability Testing. Springer. pp. 377–382
P_versus_NP_problem
Topics referred to by the same term
satisfaction measure or index (market research) Circuit satisfiability problem, a classic NP-complete problem in computer science Commonwealth Secretariat
CSAT
Boolean satisfiability problem despite there being no known efficient algorithm in the general case. The Boolean satisfiability (or SAT) problem can be
Boolean satisfiability algorithm heuristics
Boolean_satisfiability_algorithm_heuristics
Complexity class
between a problem in P and an NP-complete problem. For example, the 3-satisfiability problem, a restriction of the Boolean satisfiability problem, remains
NP-completeness
Model of computation
set is yet unknown. Circuit satisfiability Logic gate Boolean logic Switching lemma Vollmer, Heribert (1999). Introduction to Circuit Complexity. Berlin:
Boolean_circuit
Pythagorean Triples Problem via Cube-and-Conquer". In Creignou, N.; Le Berre, D. (eds.). Theory and Applications of Satisfiability Testing – SAT 2016.
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
In computer science, the Sharp Satisfiability Problem (sometimes called Sharp-SAT, #SAT or model counting) is the problem of counting the number of interpretations
♯SAT
Stochastic satisfiability Linear temporal logic satisfiability and model checking Type inhabitation problem for simply typed lambda calculus Integer circuit evaluation
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Operation in Boolean circuit theory
formula. This reduces the problem of circuit satisfiability on any circuit (including any formula) to the satisfiability problem on 3-CNF formulas. It was
Tseytin_transformation
Boolean satisfiability problem restricted to a planar incidence graph
the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence
Planar_SAT
Complexity class of problems
conditions under which classes of constrained Boolean satisfiability problems cannot be in NPI. Some problems that are considered good candidates for being NP-intermediate
NP-intermediate
Problem of finding a cycle through all vertices of a graph
The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G
Hamiltonian_path_problem
Clique problem Hamiltonian cycle problem Hamiltonian path problem Integer factorization Knapsack problem Satisfiability problem 2-satisfiability Boolean
List of computability and complexity topics
List_of_computability_and_complexity_topics
Mathematical topics based on the works of George Boole
mathematical ring for which x2 = x for every element x Boolean satisfiability problem, the problem of determining if there exists an interpretation that satisfies
Boolean
Branch of computational complexity theory
. Weighted Monotone i-Normalized Satisfiability is W[i]-complete. Weighted Monotone (i+1)-Normalized Satisfiability is in W[i]. If i>0 is odd, then antimonotone-
Parameterized_complexity
Unproven computational hardness assumption
The k {\displaystyle k} -SAT problem is a version of the Boolean satisfiability problem in which the input to the problem is a Boolean expression in conjunctive
Exponential_time_hypothesis
Subfield of automated reasoning and mathematical logic
normal form, a form in which the satisfiability of a formula is obvious. Depending on the underlying logic, the problem of deciding the validity of a formula
Automated_theorem_proving
Subunit of a computational problem
NP-completeness proofs are based on many-one reductions from 3-satisfiability, the problem of finding a satisfying assignment to a Boolean formula that
Gadget_(computer_science)
Impossible task in computing
negations, conjunctions and disjunctions combine the difficulties of satisfiability testing with that of decision of conjunctions; they are generally decided
Entscheidungsproblem
Problem in graph theory
NP-completeness of the problem can be shown, for example, by a reduction from maximum 2-satisfiability (a restriction of the maximum satisfiability problem). The weighted
Maximum_cut
Graph representing an implementation of the logical functionality of a network
emergence of much more efficient boolean satisfiability (SAT) solvers. When coupled with AIGs as the circuit representation, they lead to remarkable speedups
And-inverter_graph
Inherent difficulty of computational problems
many problems that people would like to solve efficiently, but for which no efficient algorithm is known, such as the Boolean satisfiability problem, the
Computational complexity theory
Computational_complexity_theory
Type of search algorithm
algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem. It was introduced
DPLL_algorithm
On collapse of the polynomial hierarchy if NP is in non-uniform polynomial time class
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
Karp–Lipton_theorem
Study of mathematical algorithms for optimization problems
optimization and simulated annealing. The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at
Mathematical_optimization
Electronic design automation method
algorithm cannot find one. Since the ATPG problem is NP-complete (by reduction from the Boolean satisfiability problem) there will be cases where patterns exist
Automatic test pattern generation
Automatic_test_pattern_generation
Type of quantum information processing
Adiabatic quantum computation solves satisfiability problems and other combinatorial search problems, particularly such problems that can be formulated as the
Adiabatic_quantum_computation
Process in digital electronics and integrated circuit design
Recent approaches map the optimization problem to a Boolean satisfiability problem. This allows finding optimal circuit representations using a SAT solver
Logic_optimization
Area of discrete mathematics
which are strictly compositional, graph unification is the sufficient satisfiability and combination function. Well-known applications include automatic
Graph_theory
Form of second-order logic
counting the number of solutions of the MSO formula in that case. The satisfiability problem for monadic second-order logic is undecidable in general because
Monadic_second-order_logic
circuits and algorithms for learning such circuits. AC0 Boolean circuit Circuit satisfiability Circuit value problem Parity function Håstad, Johan (1986).
Switching_lemma
Class in computational complexity theory
Horn-satisfiability – given a set of Horn clauses, is there a variable assignment that satisfies them? This is P's version of the Boolean satisfiability problem
P-complete
Concept in computational complexity theory
NEXPTIME-complete. The satisfiability problem of first-order logic with two variables is NEXPTIME-complete. The satisfiability problem of first-order logic
NEXPTIME
Computer science concept
the version of the boolean satisfiability problem for Σ k P {\displaystyle \Sigma _{k}^{\mathrm {P} }} . In this problem, we are given a Boolean formula
Polynomial_hierarchy
Computer science field
methods used BDDs. After the success of propositional satisfiability in solving the planning problem in artificial intelligence (see satplan) in 1996, the
Model_checking
Logic puzzle
puzzle is as hard to solve as the Boolean satisfiability problem, which is a well studied difficult problem in computer science. List of Nikoli puzzle
Heyawake
On domino tiling after removing two corners
Van Maaren, Hans; Warners, Joost P. (2000), "Relaxations of the satisfiability problem using semidefinite programming", Journal of Automated Reasoning
Mutilated_chessboard_problem
Computational complexity
ST-connectivity and 2-satisfiability. ST-connectivity asks, for nodes S and T in a directed graph, whether T is reachable from S. 2-satisfiability asks, given a
NL_(complexity)
American computer scientist (born 1947)
expressible as an instance of 2-satisfiability, the other solvable case of the satisfiability problem. By solving a 2-satisfiability instance to turn the given
Harry_R._Lewis
Abstract computation model
problem for alternating machines to solve is the quantified Boolean formula problem, which is a generalization of the Boolean satisfiability problem in
Alternating_Turing_machine
Standard form of Boolean function
not occur. since one way to check a CNF for satisfiability is to convert it into a DNF, the satisfiability of which can be checked in linear time 1 ≤ m
Conjunctive_normal_form
Programming paradigm based on formal logic
However, in the 1980s, the satisfiability semantics became more popular for logic programs with negation. In the satisfiability semantics, negation is interpreted
Logic_programming
Japanese computer scientist (born 1951)
Topics in his research include stable marriage, quantum circuits, the Boolean satisfiability problem, and algorithms on graphs. Iwama earned bachelor's, master's
Kazuo Iwama (computer scientist)
Kazuo_Iwama_(computer_scientist)
Graph with a median for each three vertices
solution of 2-satisfiability instances, below. Median graphs have a close connection to the solution sets of 2-satisfiability problems that can be used
Median_graph
Class of problems in computer science
PP also includes NP. To prove this, we show that the NP-complete satisfiability problem belongs to PP. Consider a probabilistic algorithm that, given a
PP_(complexity)
Stage of electronic circuit design verification
because of their efficiency and versatility. Conjunctive Normal Form Satisfiability: SAT solvers returns an assignment to the variables of a propositional
Formal_equivalence_checking
polynomial in n {\displaystyle n} that implements a verifier for the problem. That is, the circuit computes a function f ( x , y ) {\displaystyle f(x,y)} such
NP/poly
Amount of resources to perform an algorithm
other NP problem. Many combinatorial problems, such as the Knapsack problem, the travelling salesman problem, and the Boolean satisfiability problem are NP-complete
Computational_complexity
Algorithm using holographic reduction
solutions to problems without such previously known solutions for special cases of satisfiability, vertex cover, and other graph problems. They have received
Holographic_algorithm
Computer hardware technology that uses quantum mechanics
algorithms. A general class of problems to which Grover's algorithm can be applied is a Boolean satisfiability problem, where the database through which
Quantum_computing
Graph drawing with vertices on a line
exists) may be found in polynomial time by translating the problem into a 2-satisfiability problem, in which the variables represent the placement of each
Arc_diagram
Micro-electronic component
optimizing to minimize latency is an NP-complete problem equivalent to the Boolean satisfiability problem. For tasks running on processor cores, latency
System_on_a_chip
System with multiple networked computers
Marcos; Baran, Benjamin (2007). "Asynchronous team algorithms for Boolean Satisfiability". 2007 2nd Bio-Inspired Models of Network, Information and Computing
Distributed_computing
Computing using molecular biology hardware
1016/S0166-218X(96)00058-3. — Describes a solution for the Boolean satisfiability problem. Also available here: "Archived copy" (PDF). Archived from the original
DNA_computing
Logic programming with constraint satisfaction
inefficient. For this reason, an incomplete satisfiability checker may be used instead. In practice, satisfiability is checked using methods that simplify
Constraint_logic_programming
Subfield of computer science and logic
Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer". Theory and Applications of Satisfiability Testing – SAT 2016. Lecture Notes in Computer
Automated_reasoning
Proving or disproving the correctness of certain intended algorithms
Coq) or PVS), or automatic theorem provers, including in particular satisfiability modulo theories (SMT) solvers. This approach has the disadvantage that
Formal_verification
Standard form of Boolean function
Mossé, Milan; Sha, Harry; Tan, Li-Yang (2022). "A Generalization of the Satisfiability Coding Lemma and Its Applications". DROPS-IDN/V2/Document/10.4230/LIPIcs
Blake_canonical_form
Puzzle video game
method to quickly convert any Boolean circuit into such a grid that is possible if and only if the circuit is satisfiable; membership in NP is established
Minesweeper_(video_game)
Class of problems solvable in polynomial time
complexity class for problems that are not decision problems (even though, for example, finding the solution to a 2-satisfiability instance in polynomial
P_(complexity)
Task to construct a program meeting a formal specification
possible to encode program synthesis problems in Boolean logic and use algorithms for the Boolean satisfiability problem to automatically find programs. In
Program_synthesis
Logic puzzle
equivalent to arbitrary Boolean circuits, which shows NP-completeness because of the Boolean satisfiability problem. Fertin, Jamshidi, and Komusiewicz
Tentai_Show
Algebraic manipulation of "true" and "false"
is called the Boolean satisfiability problem (SAT), and is of importance to theoretical computer science, being the first problem shown to be NP-complete
Boolean_algebra
Data structure for Boolean functions
Boolean function solves the NP-complete Boolean satisfiability problem and the co-NP-complete tautology problem, constructing the BDD can take exponential
Binary_decision_diagram
American computer scientist (born 1946)
that compute Exactly-N. We have no way to prove that the Boolean satisfiability problem (often abbreviated as SAT), which is NP-complete, requires exponential
Richard_Lipton
Logical connective AND
expressions such as English "and"; In programming languages, the short-circuit and control structure; In set theory, intersection. In lattice theory,
Logical_conjunction
Hypothesis in computational complexity theory
hardness assumption, which conjectures that not only does the Boolean satisfiability problem (SAT) not have a polynomial time algorithm, it furthermore requires
Computational hardness assumption
Computational_hardness_assumption
American mathematical physicist (born 1979)
theory. He developed tensor-network formulations of Boolean satisfiability and counting problems, showing how computational complexity can be analyzed through
Jacob_Biamonte
BDD PDAG for the function f Data structure Boolean satisfiability problem Proposition Boolean circuit M. Wachter & R. Haenni, "Propositional DAGs: a New
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
Standard form of a boolean function
Boolean satisfiability problem on conjunctive normal form formulas is NP-complete. By the duality principle, so is the falsifiability problem on DNF formulas
Disjunctive_normal_form
Methods in artificial intelligence research
Satplan is an approach to planning where a planning problem is reduced to a Boolean satisfiability problem. Natural language processing focuses on treating
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Quantum computational theorem on problem complexity
the classical PCP theorem. The classical PCP theorem states that satisfiability problems like 3SAT are NP-hard when estimating the maximal number of clauses
NLTS_conjecture
deciding the satisfiability of propositional logic formula in conjunctive normal form, i.e. for solving the CNF-SAT problem Exact cover problem Min conflicts
List_of_algorithms
Measure of algorithmic complexity
diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov
Kolmogorov_complexity
Programming paradigm in which many processes are executed simultaneously
Baran, B. (29 August 2008). "Asynchronous team algorithms for Boolean Satisfiability". 2007 2nd Bio-Inspired Models of Network, Information and Computing
Parallel_computing
Graph layout on multiple half-planes
transforming the problem into an instance of the Boolean satisfiability problem and applying a SAT solver to the resulting problem. They state that their
Book_embedding
Algorithm for the minimization of Boolean functions
Mossé, Milan; Sha, Harry; Tan, Li-Yang (2022). "A Generalization of the Satisfiability Coding Lemma and Its Applications". DROPS-IDN/V2/Document/10.4230/LIPIcs
Quine–McCluskey_algorithm
List of concepts in artificial intelligence
External links satisfiability In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
System that regulates the formation of blocks on a blockchain
real-world problems, OPoW integrates multiple proof-of-work challenges—drawn from computational science problems such as Boolean satisfiability, capacitated
Proof_of_work
English mathematician and philosopher (1815–1864)
Boolean ring, a ring consisting of idempotent elements Boolean satisfiability problem Boole's syllogistic is a logic invented by 19th-century British
George_Boole
Discrete Fourier transform algorithm
unit-modulus multiplicative factors), by reduction to a satisfiability modulo theories problem solvable by brute force (Haynal & Haynal, 2011). Most of
Fast_Fourier_transform
Quantum physics-based metaheuristic for optimization problems
algorithms for solving instances of the max-SAT (maximum satisfiable problem) and Minimum Multicut problems, together with an overview of the quantum annealing
Quantum_annealing
Function returning one of only two values
Digital circuit diagram of logic gates, a Boolean circuit And-inverter graph, using only AND and NOT In order to optimize electronic circuits, Boolean
Boolean_function
Type of uncertainty of meaning where several interpretations are possible
context or a shared frame, so people cannot reliably determine what the problem is, what matters, what causes what, or what solution would count as correct
Ambiguity
Infinitely many tasks in finite time
that the lamp could have a strip of wire which, when lifted, disrupts the circuit and turns off the lamp; this strip could then be lifted by a smaller distance
Supertask
Logical connective OR
with the double pipe (||) operator. Logical disjunction is usually short-circuited; that is, if the first (left) operand evaluates to true, then the second
Logical_disjunction
Field in logic and theoretical computer science
of as a nondeterministic polynomial-time algorithm for proving non-satisfiability. That is, given a formula ϕ {\displaystyle \phi } , ϕ {\displaystyle
Proof_complexity
Representation of a graph as a path graph "thickened" by some amount
Björklund, Andreas; Husfeldt, Thore (2008), "Exact algorithms for exact satisfiability and number of perfect matchings", Algorithmica, 52 (2): 226–249, doi:10
Pathwidth
Technique for reducing number of solutions
randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem of detecting whether a Boolean formula has a unique
Isolation_lemma
Generalization of graph theory
useful in modelling such things as satisfiability problems, databases, machine learning, and Steiner tree problems. They have been extensively used in
Hypergraph
Logical operation
typewriter publications, e.g. Richard E. Ladner (January 1975). "The circuit value problem is log space complete for P". ACM SIGACT News. 7 (101): 18–20. doi:10
Negation
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Male
English
Anglicized form of Hebrew Galiyl, GALILEE means "rolling, turning" or "circuit, region, ring." In the bible, this is the name of a circuit or ring (Galilee) of the Gentiles. Not used as a personal name.
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Muslim
Problem solver
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Male
Hebrew
(גָּלִיל) Hebrew name GALIYL means "rolling, turning" or "circuit, region, ring." In the bible, this is the name of a circuit or ring (Galilee) of the Gentiles.Â
Biblical
cylinder; circuit; district; wheel
Boy/Male
Hindu, Indian
Problem
Surname or Lastname
English, Scottish, and Irish
English, Scottish, and Irish : occupational name for a player on the harp, from an agent derivative of Middle English, Middle Dutch harp ‘harp’. The harper was one of the most important figures of a medieval baronial hall, especially in Scotland and northern England, and the office of harper was sometimes hereditary. The Scottish surname is probably an Anglicized form of Gaelic Mac Chruiteir ‘son of the harper’ (from Gaelic cruit ‘harp’, ‘stringed instrument’). This surname has long been present in Ireland.
Girl/Female
Indian, Telugu
Destroyer of Problems
Male
Hebrew
Variant spelling of Hebrew Galiyl, GALIL means "rolling, turning" or "circuit, region, ring."Â
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
Boy/Male
Anglo, British, English
From the Stone Fortification
Boy/Male
Spanish
Innocent.
Boy/Male
Muslim
Caravan leader
Boy/Male
Arabic
Gazelle
Girl/Female
Indian
Goddess Durga
Surname or Lastname
English
English : from a pet form of Elis (see Ellis).Jewish (eastern Ashkenazic) : metronymic from the Yiddish female personal name Elke + the Slavic suffix -in.Jewish (eastern Ashkenazic) : patronymic from the Yiddish male personal name Elke, a pet form of Elijah + the Slavic suffix -in.
Boy/Male
Tamil
The Moon
Girl/Female
Indian, Oriya, Sikh
Remembrance; Sheet of Sweet Memory
Girl/Female
Greek
Speaker.
Male
African
a crown suits me.
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
CIRCUIT SATISFIABILITY-PROBLEM
p. pr. & vb. n.
of Short-circuit
n.
Circumlocution.
n.
A key or other device for breaking an electrical circuit.
v. t.
To travel around.
n.
Circuit; space; inclosure.
n.
Circuit; circumference.
a.
Of or pertaining to electrical tension; -- said of a supposed peculiar condition of a conducting circuit during its exposure to the action of another conducting circuit traversed by a uniform electric current when both circuits remain stationary.
n.
A district in which an itinerant preacher labors.
n.
Circuit or compass.
v. i.
To move in a circle; to go round; to circulate.
n.
Compass; circuit; inclosure.
v. t.
To join, as the electrodes of a battery or dynamo or any two points of a circuit, by a conductor of low resistance.
n.
One who travels a circuit, as a circuit judge.
n.
A certain division of a state or country, established by law for a judge or judges to visit, for the administration of justice.
n.
A kind of unraised bread, of many varieties, plain, sweet, or fancy, formed into flat cakes, and bakes hard; as, ship biscuit.
v. t.
To shift to another circuit.
n.
The act of moving or revolving around, or as in a circle or orbit; a revolution; as, the periodical circuit of the earth round the sun.
n.
A circlet.
imp. & p. p.
of Short-circuit