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Logic problem, AND of pairwise ORs
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
2-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
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
Graph with a median for each three vertices
It is also possible to define median graphs as the solution sets of 2-satisfiability problems, as the retracts of hypercubes, as the graphs of finite median
Median_graph
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
Problem in computational complexity theory
most 2 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
Maximum satisfiability problem
Maximum_satisfiability_problem
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
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
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
NL_(complexity)
Logic puzzle forming a picture in a grid
in polynomial time by transforming the problem into an instance of 2-satisfiability. An extensive comparison and discussion of nonogram solving algorithms
Nonogram
Partition of a graph whose components are reachable from all vertices
Algorithms for finding strongly connected components may be used to solve 2-satisfiability problems (systems of Boolean variables with constraints on the values
Strongly_connected_component
Directed graph representing a Boolean expression
were originally used for analyzing complex Boolean expressions. A 2-satisfiability instance in conjunctive normal form can be transformed into an implication
Implication_graph
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
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
Israeli cryptographer (born 1952)
cryptography, such as finding the first linear time algorithm for 2-satisfiability and showing the equivalence of the complexity classes PSPACE and IP
Adi_Shamir
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
Complexity class
the 3-satisfiability problem, a restriction of the Boolean satisfiability problem, remains NP-complete, whereas the slightly more restricted 2-satisfiability
NP-completeness
determining if a partially filled square can be completed) Maximum 2-satisfiability Maximum volume submatrix – Problem of selecting the best conditioned
List_of_NP-complete_problems
Directed graph isomorphic to its own transpose graph
drawing, and in the implication graphs used to efficiently solve the 2-satisfiability problem. As defined, e.g., by Goldberg & Karzanov (1996), a skew-symmetric
Skew-symmetric_graph
Independent set which is not a subset of any other independent set
or the maximal matching problem or by an N C 2 {\displaystyle NC^{2}} reduction from the 2-satisfiability problem. Typically, the structure of the algorithm
Maximal_independent_set
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
Class of problems in computer science
Each clause contains 2 literals. The satisfiability of such formulas can be decided in time linear in the number of clauses (see 2-SAT). Therefore, the
Interval_scheduling
Problem in graph theory
shown, for example, by a reduction from maximum 2-satisfiability (a restriction of the maximum satisfiability problem). The weighted version of the decision
Maximum_cut
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
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
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
Class of problems solvable in polynomial time
decision problems (even though, for example, finding the solution to a 2-satisfiability instance in polynomial time automatically gives a polynomial algorithm
P_(complexity)
Graph drawing with vertices on a line
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
Arc_diagram
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
Complexity class
a regular expression The satisfiability problem for CTL+ (computation tree logic) is 2-EXPTIME-complete. The satisfiability problem of ATL* (alternating-time
2-EXPTIME
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 Integer factorization Knapsack problem Satisfiability problem 2-satisfiability Boolean satisfiability problem Subset sum problem 3SUM Traveling salesman
List of computability and complexity topics
List_of_computability_and_complexity_topics
Graph layout on multiple half-planes
pages in a compatible way can be formulated as either an instance of 2-satisfiability, or as a problem of testing the bipartiteness of the circle graph whose
Book_embedding
(#P-complete) in many special cases for which satisfiability is tractable (in P), as well as when satisfiability is intractable (NP-complete). This includes
♯SAT
is a given edge in the minimum weight spanning forest? Exclusive or 2-satisfiability: given a formula requiring that x i {\displaystyle x_{i}} or x j {\displaystyle
SL_(complexity)
Equivalence of distributive lattices and set families
and median graphs have a dual structure as the set of solutions of a 2-satisfiability instance; Barthélemy & Constantin (1993) formulate this structure equivalently
Birkhoff's representation theorem
Birkhoff's_representation_theorem
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
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
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
Subunit of a computational problem
Many NP-completeness proofs are based on many-one reductions from 3-satisfiability, the problem of finding a satisfying assignment to a Boolean formula
Gadget_(computer_science)
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
Unproven computational hardness assumption
It states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved in subexponential time, 2 o ( n ) {\displaystyle 2^{o(n)}} . More precisely
Exponential_time_hypothesis
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
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
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
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
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
state to an accepting state. Another important NL-complete problem is 2-satisfiability (Papadimitriou 1994 Thrm. 16.3), the problem of determining whether
NL-complete
Method of automated theorem proving
a complete satisfiability algorithm for sets of propositional Horn clauses; it also generates a minimal model for the set if satisfiable: see Horn-satisfiability
Unit_propagation
whether the problem is satisfiable. Enforcing strong directional i {\displaystyle i} -consistency allows telling the satisfiability of problems that have
Local_consistency
German computer scientist (born 1955)
showed that WalkSAT, a randomized algorithm previously analyzed for 2-satisfiability by Papadimitriou, had good expected time complexity (although still
Uwe_Schöning
On linear-time algorithms for graph logic
underlying dynamic programming algorithm for Boolean satisfiability problem with one for Maximum satisfiability problem or ♯SAT, one immediately obtains corresponding
Courcelle's_theorem
Operation in Boolean circuit theory
This reduces the problem of circuit satisfiability on any circuit (including any formula) to the satisfiability problem on 3-CNF formulas. It was discovered
Tseytin_transformation
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)
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
Linux package management library
repositories takes only milliseconds. Using satisfiability for computing package dependencies. The Boolean satisfiability problem is a well-researched problem
ZYpp
Mathematical method in statistical physics
(2005). "Survey propagation: An algorithm for satisfiability". Random Structures and Algorithms. 27 (2): 201–226. arXiv:cs.CC/0212002. doi:10.1002/rsa
Cavity_method
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
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
Some important problems about two-variable logic, such as satisfiability and finite satisfiability, are decidable. This result generalizes results about the
Two-variable_logic
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
SMT solver
mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are
Cooperating_Validity_Checker
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
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
Type of quantum information processing
model or a QUBO problem. Satisfiability problems seek a state that satisfies C 1 ∧ C 2 ∧ ⋯ ∧ C M {\displaystyle C_{1}\wedge C_{2}\wedge \cdots \wedge C_{M}}
Adiabatic_quantum_computation
incomplete block designs (PBIBDs) Block walking Boolean satisfiability problem 2-satisfiability 3-satisfiability Bracelet (combinatorics) Bruck–Chowla–Ryser theorem
Index of combinatorics articles
Index_of_combinatorics_articles
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
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
Logical connective AND
LOGICAL AND): ⋀ i = 1 n a i = a 1 ∧ a 2 ∧ … a n − 1 ∧ a n {\displaystyle \bigwedge _{i=1}^{n}a_{i}=a_{1}\wedge a_{2}\wedge \ldots a_{n-1}\wedge a_{n}} In
Logical_conjunction
computational complexity theory that is a maximization version of the Boolean satisfiability problem 3SAT. In MAXEkSAT, each clause has exactly k literals, each
MAXEkSAT
Can one split the integers into two sets such that every Pythagorean triple spans both?
trillion (still highly complex) cases, and those, expressed as Boolean satisfiability problems, were examined using a SAT solver. Creating the proof took
Boolean Pythagorean triples problem
Boolean_Pythagorean_triples_problem
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)
The network flow algorithms are used to solve instances of weighted 2-satisfiability, and these in turn are used to compute utilitarian stable matchings
Optimal_stable_matching
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
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
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
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
Problem in computational complexity theory
archival service (link). Erickson, Jeff (1999), "Lower bounds for linear satisfiability problems", Chicago Journal of Theoretical Computer Science, 1999, MIT
3SUM
Books about algorithms by Donald Knuth
Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was released
The Art of Computer Programming
The_Art_of_Computer_Programming
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
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
Seven mathematical problems with a US$1 million prize for each solution
common example of an NP problem not known to be in P is the Boolean satisfiability problem. Most mathematicians and computer scientists expect that P ≠ NP;
Millennium_Prize_Problems
properties by using refinement types. Properties are verified using a satisfiability modulo theories (SMT) solver which is SMTLIB2-compliant, such as the
Liquid_Haskell
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
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
Computer hardware technology that uses quantum mechanics
of problems to which Grover's algorithm can be applied is a Boolean satisfiability problem, where the database through which the algorithm iterates is
Quantum_computing
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
Discrete Fourier transform algorithm
flowgraphs with unit-modulus multiplicative factors), by reduction to a satisfiability modulo theories problem solvable by brute force (Haynal & Haynal, 2011)
Fast_Fourier_transform
Complexity class of problems
theorem provides conditions under which classes of constrained Boolean satisfiability problems cannot be in NPI. Some problems that are considered good candidates
NP-intermediate
Method of deriving conclusions
Kouri Kissel 2024, Lead section, § 2. Language Sider 2010, pp. 90–95 Cook 2009, pp. 119–120 Garson 2024, Lead section, § 2. Modal Logics Sider 2010, pp. 133–136
Rule_of_inference
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
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
Computer scientist
gives a linear time algorithm for Horn-satisfiability.[DG84] This is a variant of the Boolean satisfiability problem: its input is a Boolean formula
Jean_Gallier
Estimate of time taken for running an algorithm
time 2 f ( k ) ⋅ poly ( n ) {\displaystyle 2^{f(k)}\cdot {\textsf {poly}}(n)} . The exponential time hypothesis (ETH) is that 3SAT, the satisfiability problem
Time_complexity
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
Computation model defining an abstract machine
logical expression to decide by finitely many operations its validity or satisfiability ... The Entscheidungsproblem must be considered the main problem of
Turing_machine
Probabilistic optimization technique and metaheuristic
is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For
Simulated_annealing
Topics referred to by the same term
Davis–Putnam–Logemann–Loveland algorithm, an algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form Delay-locked
DLL
American computer scientist and mathematician (born 1938)
——— (2015). The Art of Computer Programming. Vol. 4, Fascicle 6: Satisfiability. Addison-Wesley. ISBN 978-0-134-39760-3. ——— (2025). The Art of Computer
Donald_Knuth
2 SATISFIABILITY
2 SATISFIABILITY
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
English
English : variant of Garrett 2.
Surname or Lastname
Variant of Nicolai 2.English
Variant of Nicolai 2.English : variant of Nicholas.
Surname or Lastname
English
English : variant of Land 2.
Surname or Lastname
English
English : variant of Haddock 2.
Surname or Lastname
English
English : variant of Glad 2.
Surname or Lastname
English
English : variant of Greenfield 2.
Surname or Lastname
English
English : patronymic from Lakin 2.
Surname or Lastname
English
English : variant of Maul 2.
Surname or Lastname
English
English : variant of Goodall 2.
Surname or Lastname
North German variant of Laas 2.Jewish (Ashkenazic)
North German variant of Laas 2.Jewish (Ashkenazic) : unexplained.English : nickname from Middle English lesse, lasse ‘smaller’ (from Old English lǣssa ‘less’), perhaps also used in the sense ‘younger’.
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
English
English : variant of Hayden 2.
Surname or Lastname
English
English : variant of Hackett 2.
Surname or Lastname
English
English : variant of Diamond 2.
Girl/Female
Indian
Mixture of 2 Names
Surname or Lastname
English
English : patronymic from Lamb 2.
Boy/Male
Shakespearean
King Henry IV, Part 1' Earl of March. Scroop.
Surname or Lastname
English
English : variant of Mixon 2.
2 SATISFIABILITY
2 SATISFIABILITY
Girl/Female
Australian, Greek, Russian
Light; Torch; Moon Elope
Boy/Male
Latin
Name of a Greek author.
Boy/Male
English
Burnt wood.
Female
English
Elaborated form of English Janet, JANETTE means "God is gracious."
Boy/Male
French
Knight.
Boy/Male
Australian, Czech, Czechoslovakian, German, Polish, Teutonic
Frenchman; Free; From France
Girl/Female
Spanish American English German
Pretty.
Male
Hindi/Indian
Variant spelling of Hindi Mahendra, MAHINDER means "great-Indra."
Boy/Male
American, Australian, British, Christian, English, French, German, Greek
Lover of Horses; Form of Phillip
Boy/Male
Tamil
Full of Joy
2 SATISFIABILITY
2 SATISFIABILITY
2 SATISFIABILITY
2 SATISFIABILITY
2 SATISFIABILITY
n.
See Sloough, 2.
n.
See Statistics, 2.
n.
See Stylet, 2.
n.
See Viol, 2.
n.
See Stripping, 2.
n.
See Topsman, 2.
n.
See Ringtail, 2.
n. pl.
See Rostrum, 2.
n.
See Umbra, 2.
n.
See Stylet, 2.
n.
See Grasshopper, 2.
n.
The bonito, 2.
n.
Sewerage, 2.
n.
See Lycanthropy, 2.
n.
See Hermes, 2.
n.
See Hoarding, 2.
n.
Sameness, 2.
n.
See Macaroon, 2.
n.
See Transom, 2.
n.
See Limiter, 2.