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Existence of values making formula true
meaning by providing additional axioms. The satisfiability modulo theories problem considers satisfiability of a formula with respect to a formal theory
Satisfiability
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
problems, which are NP-complete, 2-satisfiability can be solved in polynomial time. Instances of the 2-satisfiability problem are typically expressed as
2-satisfiability
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
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem in NP
Cook–Levin_theorem
Problem in formal logic
survey. The problem of Horn satisfiability is solvable in linear time. A polynomial-time algorithm for Horn satisfiability is recursive: A first termination
Horn-satisfiability
computational complexity, not-all-equal 3-satisfiability (NAE3SAT) is an NP-complete variant of the Boolean satisfiability problem, often used in proofs of NP-completeness
Not-all-equal 3-satisfiability
Not-all-equal_3-satisfiability
Problem in computational complexity theory
literals, as in 2-satisfiability, we get the MAX-2SAT problem. If they are restricted to at most 3 literals per clause, as in 3-satisfiability, we get the MAX-3SAT
Maximum satisfiability problem
Maximum_satisfiability_problem
Set of computational problems stated by Richard Karp (1973)
to be NP-complete by reducing Exact cover to Knapsack. Satisfiability: the Boolean satisfiability problem for formulas in conjunctive normal form (often
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
In logic, a statement which is always true
whether there is any valuation that makes a formula true is the Boolean satisfiability problem; the problem of checking tautologies is equivalent to this problem
Tautology_(logic)
Logical formulation of graph properties
problem of satisfiability concerns testing whether there exists a graph that models a given sentence. Although both model checking and satisfiability are hard
Logic_of_graphs
Unsolved problem in computer science
transformed mechanically into a Boolean satisfiability problem in polynomial time. The Boolean satisfiability problem is one of many NP-complete problems
P_versus_NP_problem
Type of search algorithm
is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for
DPLL_algorithm
Classic NP-complete problem in computer science
CircuitSAT can be reduced to the other satisfiability problems to prove their NP-completeness. The satisfiability of a circuit containing m {\displaystyle
Circuit satisfiability problem
Circuit_satisfiability_problem
Formalism of first-order logic
same as the satisfiability of ∀ x ∃ y R ( x , y ) {\displaystyle \forall x\exists yR(x,y)} . At the meta-level, first-order satisfiability of a formula
Skolem_normal_form
Computer program for the Boolean satisfiability problem
a SAT solver is a computer program which aims to solve the Boolean satisfiability problem (SAT). On input a formula over Boolean variables, such as "(x
SAT_solver
American electrical engineer and computer scientist
high-performance Boolean satisfiability solvers." In 2012, Sakallah became an ACM Fellow "for algorithms for Boolean Satisfiability that advanced the state-of-the-art
Karem_A._Sakallah
Domination analysis of an approximation algorithm is a way to estimate its performance, introduced by Glover and Punnen in 1997. Unlike the classical approximation
Domination_analysis
Method for automated planning
Planning as Satisfiability) is a method for automated planning. It converts the planning problem instance into an instance of the Boolean satisfiability problem
Satplan
Input where a function output does not matter
In digital logic, a don't-care term (abbreviated DC, historically also known as redundancies, irrelevancies, optional entries, invalid combinations, vacuous
Don't-care_term
Unproven computational hardness assumption
that was formulated by Impagliazzo & Paturi (1999). It states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved in subexponential
Exponential_time_hypothesis
NP-complete variant of the Boolean satisfiability problem
Boolean satisfiability problem All the rules can be proved by the table of truth. Schaefer, Thomas J. (1978). "The complexity of satisfiability problems"
1-in-3-SAT
Software for solving satisfiability problems
Z3, also known as the Z3 Theorem Prover, is a satisfiability modulo theories (SMT) solver developed by Microsoft. Z3 was developed in the Research in Software
Z3_Theorem_Prover
Concept in first-order logic
or instantiation. The satisfiability problem for this class is NEXPTIME-complete. Efficient algorithms for deciding satisfiability of EPR have been integrated
Bernays–Schönfinkel_class
whether the problem is satisfiable. Enforcing strong directional i {\displaystyle i} -consistency allows telling the satisfiability of problems that have
Local_consistency
of the Boolean satisfiability problem despite there being no known efficient algorithm in the general case. The Boolean satisfiability (or SAT) problem
Boolean satisfiability algorithm heuristics
Boolean_satisfiability_algorithm_heuristics
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
Version of classical propositional calculus that uses only one connective
ax 3 P→R mp 9,10 qed Satisfiability in the implicational propositional calculus is trivial, because every formula is satisfiable: just set all variables
Implicational propositional calculus
Implicational_propositional_calculus
the server requires that images use a different format. 416 Range Not Satisfiable The client has asked for a portion of the file (byte serving), but the
List_of_HTTP_status_codes
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
SAT solving algorithm
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
Conflict-driven clause learning
Conflict-driven_clause_learning
HTTP facility to fetch a specific part of a file
range is invalid, the server responds with a 416 Requested Range Not Satisfiable status code. Clients which request byte-serving might do so in cases
Byte_serving
Complexity class used to classify decision problems
k and f dividing n? Every NP-complete problem is in NP. The Boolean satisfiability problem (SAT), where we want to know whether or not a certain formula
NP_(complexity)
Non-contradiction of a theory
theory is a syntactic notion, whose semantic counterpart is satisfiability. A theory is satisfiable if it has a model, i.e., there exists an interpretation
Consistency
Complexity class
the satisfiability of a Boolean formula in disjunctive normal form is easy: such a formula is satisfiable if and only if it contains a satisfiable conjunction
♯P-complete
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
Complexity class
NP-complete problem. For example, the 3-satisfiability problem, a restriction of the Boolean satisfiability problem, remains NP-complete, whereas the
NP-completeness
Local search algorithm solving boolean satisfiability
into Boolean satisfiability problems is called satplan. MaxWalkSAT is a variant of WalkSAT designed to solve the weighted satisfiability problem, in which
WalkSAT
Algorithm for statistical inference on graphical models
low-density parity-check codes, turbo codes, free energy approximation, and satisfiability. The algorithm was first proposed by Judea Pearl in 1982, who formulated
Belief_propagation
Argument whose conclusion must be true if its premises are
arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's
Validity_(logic)
When a finite set S of relations yields polynomial-time or NP-complete problems
Schaefer's dichotomy theorem include the NP-completeness of SAT (the Boolean satisfiability problem) and its two popular variants 1-in-3 SAT and not-all-equal 3SAT
Schaefer's_dichotomy_theorem
Books about algorithms by Donald Knuth
Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was released in December 2015; Volume 4, Fascicle 5 ("Mathematical
The Art of Computer Programming
The_Art_of_Computer_Programming
Subfield of automated reasoning and mathematical logic
a Herbrand universe and a Herbrand interpretation that allowed (un)satisfiability of first-order formulas (and hence the validity of a theorem) to be
Automated_theorem_proving
Concept in the Boolean satisfiability problem
(PDF). In Biere, A.; Gomes, C.P. (eds.). Theory and Applications of Satisfiability Testing — SAT 2006. Lecture Notes in Computer Science. Vol. 4121. Springer
Unsatisfiable_core
complexity, XOR-SAT (also known as XORSAT) is the class of boolean satisfiability problems where each clause contains XOR (i.e. exclusive or, written
XOR-SAT
the Satisfiability Problem. GRASP home page J.P. Marques-Silva; Karem A. Sakallah (November 1996). "GRASP-A New Search Algorithm for Satisfiability". Digest
GRASP_(SAT_solver)
On linear-time algorithms for graph logic
is undecidable. However, satisfiability of MSO2 formulas is decidable for the graphs of bounded treewidth, and satisfiability of MSO1 formulas is decidable
Courcelle's_theorem
If there is a polynomial time algorithm for unambiguous-SAT, then NP equals RP
published in 1986. The Valiant–Vazirani theorem implies that the Boolean satisfiability problem, which is NP-complete, remains a computationally hard problem
Valiant–Vazirani_theorem
Set of objects whose state must satisfy limits
tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP)
Constraint satisfaction problem
Constraint_satisfaction_problem
Type of quantum information processing
at the tipping points smaller. Adiabatic quantum computation solves satisfiability problems and other combinatorial search problems, particularly such
Adiabatic_quantum_computation
Topics referred to by the same term
cartoonist Bob Satterfield .SAT, a file extension for ACIS CAD files Boolean satisfiability problem (SAT, 2-SAT, 3-SAT) SCSI / ATA Translation, a computer device
SAT_(disambiguation)
Mathematical topics based on the works of George Boole
ring, a mathematical ring for which x2 = x for every element x Boolean satisfiability problem, the problem of determining if there exists an interpretation
Boolean
Topics referred to by the same term
Icarus Falls, 2018 Satisfactory, a 2024 factory simulation video game Satisfiability, a property pertaining to mathematical formulas Satisfy (disambiguation)
Satisfaction
Computational Formula that can be measured in terms of True or False
quantified Boolean formula problem (QBF) is a generalization of the Boolean satisfiability problem in which both existential quantifiers and universal quantifiers
True quantified Boolean formula
True_quantified_Boolean_formula
Computational problem
respect to AC0 reductions. The problem is closely related to the Boolean satisfiability problem which is complete for NP and its complement, the propositional
Circuit_value_problem
Task to construct a program meeting a formal specification
synthesis problems in Boolean logic and use algorithms for the Boolean satisfiability problem to automatically find programs. In 2013, a unified framework
Program_synthesis
Fragment of metric temporal logic
problem of deciding whether a MITL formula is satisfiable over a signal is EXPSPACE-complete, while satisfiability for MITL0,∞ is PSPACE-complete. R. Alur,
Metric interval temporal logic
Metric_interval_temporal_logic
Complexity class
of an NP-complete problem is the Boolean satisfiability problem: given a Boolean formula, is it satisfiable (is there a possible input for which the formula
Co-NP
Problem in computer science
complexity subfield of computer science. It generalises the Boolean satisfiability problem (SAT) which is a decision problem considered in complexity theory
MAX-3SAT
Boolean satisfiability problem restricted to a planar incidence graph
science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar
Planar_SAT
problem, the difference-map algorithm has been used for the boolean satisfiability problem, protein structure prediction, Ramsey numbers, diophantine equations
Difference-map_algorithm
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
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
Linux package management library
repositories takes only milliseconds. Using satisfiability for computing package dependencies. The Boolean satisfiability problem is a well-researched problem
ZYpp
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
Area of mathematical logic
in the proof. The completeness theorem allows us to transfer this to satisfiability. However, there are also several direct (semantic) proofs of the compactness
Model_theory
British computer scientist
the areas of social choice, constraint programming and propositional satisfiability. He has served on the Executive Council of the Association for the Advancement
Toby_Walsh
Existence and cardinality of models of logical theories
can be derived using the deduction rules for first-order logic) and satisfiability (there is a model). Somewhat surprisingly, even before the completeness
Löwenheim–Skolem_theorem
\beta _{1},\beta _{2}} are in S. If a set S is a Hintikka set, then S is satisfiable. Smullyan, Raymond (2014). A Beginner's Guide to Mathematical Logic.
Hintikka_set
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
Tool for proving a logical formula
literally, these two formulae are not the same as for satisfiability: rather, the satisfiability P ( x , y ) ∨ Q ( f ( x ) ) {\displaystyle P(x,y)\lor
Method_of_analytic_tableaux
Complexity class
halting problem is NP-hard but not NP-complete. For example, the Boolean satisfiability problem can be reduced to the halting problem by transforming it to
NP-hardness
formula is refutable, the original φ was as well; the same is true of satisfiability, since we may take a quotient of satisfying model of the new formula
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
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
Finite-state machine
Verwer: the minimal DFA identification problem is reduced to deciding the satisfiability of a Boolean formula. The main idea is to build an augmented prefix-tree
Deterministic finite automaton
Deterministic_finite_automaton
Type of logical system
from model theory, where M ⊨ ϕ {\displaystyle M\vDash \phi } denotes satisfiability in a model, i.e. "there is a suitable assignment of values in M {\displaystyle
First-order_logic
Symbol used in mathematics and logic
Enrico; Tacchella, Armando (2004-02-24). Theory and Applications of Satisfiability Testing: 6th International Conference, SAT 2003. Santa Margherita Ligure
Up_tack
System of formal deduction in logic
arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's
Hilbert_system
placed, then it may be solved efficiently by using an instance of 2-satisfiability to find a placement avoiding any conflicting pairs of placements; several
Automatic_label_placement
allocation problem Betweenness Assembling an optimal Bitcoin block. Boolean satisfiability problem (SAT). There are many variations that are also NP-complete.
List_of_NP-complete_problems
American mathematician and philosopher (1926–2016)
Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth
Hilary_Putnam
Variable that stores data about other variables or program structure
arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's
Metavariable
properties by using refinement types. Properties are verified using a satisfiability modulo theories (SMT) solver which is SMTLIB2-compliant, such as the
Liquid_Haskell
Meta-algorithmic technique to choose an algorithm
optimized. A well-known application of algorithm selection is the Boolean satisfiability problem. Here, the portfolio of algorithms is a set of (complementary)
Algorithm_selection
Functional programming language inspired by ML and aimed at program verification
prove that programs meet their specifications using a combination of satisfiability modulo theories (SMT) solving and manual proofs. For execution, programs
F*_(programming_language)
Mathematical method in statistical physics
method has proved useful in solving optimization problems such as k-satisfiability and graph coloring. It has yielded not only ground states energy predictions
Cavity_method
Programming algorithm
Chaff is an algorithm for solving instances of the Boolean satisfiability problem in programming. It was designed by researchers at Princeton University
Chaff_algorithm
Theorem in mathematical logic
sentences that is not satisfiable. A {\displaystyle A} must contain ¬ φ {\displaystyle \lnot \varphi } because otherwise it would be satisfiable. Because adding
Compactness_theorem
Method for problem solving in optimization
the target is to minimize the total length of the cycle The Boolean satisfiability problem, in which a candidate solution is a truth assignment, and the
Local_search_(optimization)
American mathematician
his dichotomy theorem, stating that any problem generalizing Boolean satisfiability in a certain way is either in the complexity class P or is NP-complete
Thomas_Jerome_Schaefer
Mathematical model for deduction or proof systems
arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's
Formal_system
Graph with a median for each three vertices
the solution of 2-satisfiability instances, below. Median graphs have a close connection to the solution sets of 2-satisfiability problems that can be
Median_graph
Topics referred to by the same term
Romania Customer satisfaction measure or index (market research) Circuit satisfiability problem, a classic NP-complete problem in computer science Commonwealth
CSAT
Code-breaking game
consistent with the hints in the previous guesses). The Mastermind satisfiability problem (MSP) is a decision problem that asks, "Given a set of guesses
Mastermind_(board_game)
Proof that only uses basic techniques
arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's
Elementary_proof
Class of problems in computer science
can be shown by a reduction from the following version of the Boolean satisfiability problem, which was shown to be NP-complete likewise to the unrestricted
Interval_scheduling
than the full language, The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the
Fragment_(logic)
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
Topics referred to by the same term
automatic digital computer created by Konrad J Zuse Z3 Theorem Prover, a satisfiability modulo theories solver by Microsoft .Z3, a file extension for story
Z3
Computer science concept
complete problem for Σ k P {\displaystyle \Sigma _{k}^{\mathrm {P} }} is satisfiability for quantified Boolean formulas with k – 1 alternations of quantifiers
Polynomial_hierarchy
SATISFIABILITY
SATISFIABILITY
SATISFIABILITY
SATISFIABILITY
Female
African
joy; valued; or, born on the road.
Girl/Female
Dutch
Reknown defender.
Girl/Female
American, Australian, Hungarian
Rose; Lilly
Boy/Male
African, Finnish, Hindu, Indian, Japanese, Tamil
Autumn; Bright; Short Form of Joakim; Established by God
Boy/Male
Hindu, Indian
Golden
Boy/Male
Tamil
Nithalaksh | நீதாலாகà¯à®·
Boy/Male
Arabic
Innocence; Pure
Girl/Female
Indian
She was a companion
Boy/Male
Indian, Sanskrit
Wrigveda
Girl/Female
Latin
Protector.
SATISFIABILITY
SATISFIABILITY
SATISFIABILITY
SATISFIABILITY
SATISFIABILITY