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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
Existence of values making formula true
additional axioms. The satisfiability modulo theories problem considers satisfiability of a formula with respect to a formal theory, which is a (finite or
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
by using refinement types. Properties are verified using a satisfiability modulo theories (SMT) solver which is SMTLIB2-compliant, such as the Z3 Theorem
Liquid_Haskell
SMT solver
mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and
Cooperating_Validity_Checker
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
Proving or disproving the correctness of certain intended algorithms
PVS), or automatic theorem provers, including in particular satisfiability modulo theories (SMT) solvers. This approach has the disadvantage that it may
Formal_verification
Set of objects whose state must satisfy limits
kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer
Constraint satisfaction problem
Constraint_satisfaction_problem
Problem in computational complexity theory
is not empty. Boolean Satisfiability Problem Constraint satisfaction Satisfiability modulo theories http://www.satisfiability.org/ https://web.archive
Maximum satisfiability problem
Maximum_satisfiability_problem
Functional programming language inspired by ML and aimed at program verification
that programs meet their specifications using a combination of satisfiability modulo theories (SMT) solving and manual proofs. For execution, programs written
F*_(programming_language)
In mathematical logic, a well-formed formula with no free variables
discover interpretations of theories that render all sentences as being true is known as the satisfiability modulo theories problem. For the interpretation
Sentence_(mathematical_logic)
Computer program for the Boolean satisfiability problem
intended behavior. SAT solvers are the core component on which satisfiability modulo theories (SMT) solvers are built, which are used for problems such as
SAT_solver
Compile-time transformation
Polymorphism" (PDF). Proceedings of the 12th International Workshop on Satisfiability Modulo Theories, (SMT 2014). Archived (PDF) from the original on 2023-10-03
Monomorphization
SMT solver for software verification
formal program verification. It operates on the principle of satisfiability modulo theories (SMT). Development was undertaken by researchers at the Paris-Sud
Alt-Ergo
American electrical engineer and computer scientist
computational logic, functional verification, SAT solvers, satisfiability modulo theories, and the Graph automorphism problem. He was elevated to the
Karem_A._Sakallah
Type of search algorithm
application that often involves DPLL is automated theorem proving or satisfiability modulo theories (SMT), which is a SAT problem in which propositional variables
DPLL_algorithm
Topics referred to by the same term
digital computer created by Konrad J Zuse Z3 Theorem Prover, a satisfiability modulo theories solver by Microsoft .Z3, a file extension for story files for
Z3
Software for a class of mathematical problems
problem resolution. Satisfiability modulo theories for solvers of logical formulas with respect to combinations of background theories expressed in classical
Solver
Condition of an optimization problem which the solution must satisfy
Level set Linear programming Nonlinear programming Restriction Satisfiability modulo theories Takayama, Akira (1985). Mathematical Economics (2nd ed.). New
Constraint_(mathematics)
Higher-order logic (HOL) automated theorem prover
through the Sledgehammer proof-automation interface, external satisfiability modulo theories (SMT) solvers (including CVC4) and resolution-based automated
Isabelle_(proof_assistant)
Topics referred to by the same term
Indonesia Shanghai maglev train, a Transrapid line in China Satisfiability modulo theories, in computer science and logic Simultaneous multithreading,
SMT
Area of mathematical logic
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing
Model_theory
Computer programming paradigm
Mathematical optimization Nurse scheduling problem Regular constraint Satisfiability modulo theories Traveling tournament problem Rossi, Francesca; Beek, Peter van;
Constraint_programming
Discrete Fourier transform algorithm
with unit-modulus multiplicative factors), by reduction to a satisfiability modulo theories problem solvable by brute force (Haynal & Haynal, 2011). Most
Fast_Fourier_transform
Graph data structure
Computer Science. Proceedings of the 5th International Workshop on Satisfiability Modulo Theories (SMT 2007). 198 (2): 19–35. doi:10.1016/j.entcs.2008.04.078
E-graph
Symbol representing a mathematical concept
include satisfiability modulo theories solvers. Algebraic data type Initial algebra Logical connective Logical constant Term algebra Theory of pure equality
Function_symbol
Interactive theorem prover software
for a computer-based database of all mathematical knowledge Satisfiability modulo theories – Logical problem studied in computer science Ornes, Stephen
Proof_assistant
Formally verified capability-based microkernel
providing correct implementation of the sel4 hardware by using Satisfiability Modulo Theories (SMT) verification tools. Main building blocks of the proposed
SeL4
Mathematical software
proving Algebraic modeling language Constraint-logic programming Satisfiability modulo theories van Hulzen, J. A.; Calmet, J. (1983). "Computer Algebra Applications"
Computer_algebra_system
portraits and ubiquitous computing Greg Nelson (at PARC 1980–1981), satisfiability modulo theories, extended static checking, program verification, Modula-3, theorem
List of people associated with PARC
List_of_people_associated_with_PARC
Project for an open source artificial intelligence framework
reduction. A collection of pre-defined atoms that encode a satisfiability modulo theories solver, built in as a part of a generic graph query engine,
OpenCog
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
Research operating system from Microsoft Research
which proves the Nucleus correct using the Z3 Theorem Prover satisfiability modulo theories (SMT) automated theorem prover (solver). The Nucleus relies
Verve_(operating_system)
Annual automated theorem proving competition
fields, in particular the successful SMT-COMP competition for satisfiability modulo theories, the SAT Competition for propositional reasoners, and the modal
CADE_ATP_System_Competition
Algorithm to solve SMT problems
1007/11513988_33. ISBN 9783540316862. Reynolds, Andrew (2015). "Satisfiability Modulo Theories and DPLL(T)" (PDF). The University of Iowa. Retrieved 2019-04-08
DPLL(T)
Process in artificial intelligence and operations research
(mathematics) Candidate solution Boolean satisfiability problem Decision theory Satisfiability modulo theories Knowledge-based configuration Tsang, Edward
Constraint_satisfaction
American computer scientist
was also an early contributor to the research field known as satisfiability modulo theories (SMT), supervising the development of several early SMT solvers:
David_L._Dill
Relationship between the technology company and the open source software paradigm
Microsoft open sourced the Z3 Theorem Prover, a cross-platform satisfiability modulo theories (SMT) solver. Also in 2015, Microsoft co-founded the Node.js
Microsoft_and_open_source
authoring system for interactive fiction Greg Nelson (1953–2015) – satisfiability modulo theories, extended static checking, program verification, Modula-3 committee
List_of_programmers
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
Automatic detection of the type of an expression in a formal language
for type inference are based on constraint satisfaction or satisfiability modulo theories. As an example, the Haskell function map applies a function
Type_inference
Decidable first-order theory of the natural numbers with addition
satisfiability modulo theories solvers use complete integer programming techniques to handle quantifier-free fragment of Presburger arithmetic theory
Presburger_arithmetic
Reformulation of Floyd-Hoare logic
check assertions in programs using a theorem-prover (like a satisfiability modulo theories (SMT) solver or interactive theorem proving assistant): see
Predicate transformer semantics
Predicate_transformer_semantics
(#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
Standard system of axiomatic set theory
set theories: Morse–Kelley set theory Von Neumann–Bernays–Gödel set theory Tarski–Grothendieck set theory Constructive set theory Internal set theory At
Zermelo–Fraenkel_set_theory
Set of the elements not in a given subset
of 3, then the complement of B is the set of numbers congruent to 1 or 2 modulo 3 (or, in simpler terms, the integers that are not multiples of 3). Assume
Complement_(set_theory)
"pioneering contributions to the foundations of the theory and practice of satisfiability modulo theories (SMT)”. Several software tools (a SAT solver, and
Ofer_Strichman
Architecture and Methodology (GERAM) Greg Nelson (1953–2015) – satisfiability modulo theories, extended static checking, program verification, Modula-3 committee
List_of_computer_scientists
American computer scientist
automated theorem proving, especially in the area now named satisfiability modulo theories, where he contributed techniques for combining decision procedures
Greg Nelson (computer scientist)
Greg_Nelson_(computer_scientist)
Partition of a graph's nodes into 2 disjoint subsets
P. (1995), "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming", Journal of the ACM, 42 (6):
Cut_(graph_theory)
Study of computable functions and Turing degrees
these structures is that one of computably enumerable sets under inclusion modulo finite difference; in this structure, A is below B if and only if the set
Computability_theory
Simplification technique in mathematical logic
{\displaystyle \alpha _{QF}} without quantifiers that is equivalent to it (modulo this theory). An example from mathematics says that a single-variable quadratic
Quantifier_elimination
Cube-and-Conquer". In Creignou, N.; Le Berre, D. (eds.). Theory and Applications of Satisfiability Testing – SAT 2016. Lecture Notes in Computer Science
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Complexity class of problems
{\displaystyle y} have a divisor congruent to 1 modulo x {\displaystyle x} ? IMSAT, the Boolean satisfiability problem for "intersecting monotone CNF": conjunctive
NP-intermediate
Unsolved problem in computational complexity theory
NP-hard. Consider the following system of linear equations over the integers modulo k {\displaystyle k} : a 1 x 1 ≡ b 1 ⋅ x 2 + c 1 ( mod k ) , a 2 x 2 ≡ b
Unique_games_conjecture
Family of formal systems
equality. This conversion allows the K Framework to use existing Satisfiability modulo theories (SMT) solvers. These solvers help to find proofs for theorems
Matching_logic
Maximal proper filter
in set theory, model theory, and topology. Usually, only free ultrafilters lead to non-trivial constructions. For example, an ultraproduct modulo a principal
Ultrafilter_on_a_set
System of mathematical set theory
1}. We apply the axiom of foundation to get a function that gives ( k modulo 2 ) for k ≤ n for each n in ω. Then we use Δ0-collection to send ⟨ n, 0
Kripke–Platek_set_theory
Equations in differential cryptanalysis
cryptanalysis that mix additions over two different groups (e.g. addition modulo 232 and addition over GF(2)) and where input and output differences are
Differential equations of addition
Differential_equations_of_addition
Assignment of meaning to the symbols of a formal language
used, but rather D modulo an equivalence relation definable in A. For additional information, see Interpretation (model theory). A theory T is said to interpret
Interpretation_(logic)
Mathematical construction
( M i ) i ∈ I {\displaystyle M_{\bullet }=\left(M_{i}\right)_{i\in I}} modulo U {\displaystyle {\mathcal {U}}} is the quotient set of ∏ i ∈ I M i {\displaystyle
Ultraproduct
Inference rule in logic, proof theory, and automated theorem proving
for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis
Resolution_(logic)
Algorithmic process of solving equations
semantic or equational unification, or E-unification, or unification modulo theory. If the right side of each equation is closed (no free variables), the
Unification (computer science)
Unification_(computer_science)
tuples a of A); φ is equivalent modulo T to a formula ψ in L. Less formally: a property is implicitly definable in a theory in language L (via a formula
Beth_definability
Undecidable decision problem introduced by Emil Post
problem is NP-complete. Unlike some NP-complete problems like the boolean satisfiability problem, a small variation of the bounded problem was also shown to
Post_correspondence_problem
Methodic assignment of colors to elements of a graph
colors where Z k {\displaystyle \mathbb {Z} _{k}} is the set of integers modulo k {\displaystyle k} consisting of the elements (or colors) 0 , 1 , 2 ,
Graph_coloring
number theory. 1., an introduction. Springer. p. 322. ISBN 978-3-642-75462-3. Milchior, Arthur (January 2017). "Undecidability of satisfiability of expansions
Regular_numerical_predicate
Algebraic manipulation of "true" and "false"
a way as to make the formula evaluate to true is called the Boolean satisfiability problem (SAT), and is of importance to theoretical computer science
Boolean_algebra
Generalization of graph theory
morphisms. Undirected hypergraphs are useful in modelling such things as satisfiability problems, databases, machine learning, and Steiner tree problems. They
Hypergraph
Function returning one of only two values
the operators in a Boolean formula. When the coefficients are calculated modulo 2 one obtains the algebraic normal form (Zhegalkin polynomial). Direct expressions
Boolean_function
Mathematical concept for comparing objects
angles. Given a natural number n {\displaystyle n} , "is congruent to, modulo n {\displaystyle n} " on the integers. "Have the same length and direction"
Equivalence_relation
Branch of mathematical logic
effective Polish spaces, can be represented as sets of natural numbers, and modulo this representation can be studied in second-order arithmetic. Reverse mathematics
Reverse_mathematics
Chaff algorithm: an algorithm for solving instances of the Boolean satisfiability problem Davis–Putnam algorithm: check the validity of a first-order
List_of_algorithms
Mathematical use of "for all" and "there exists"
{\displaystyle \alpha _{QF}} without quantifiers that is equivalent to it (modulo this theory). Every quantification involves one specific variable and a domain
Quantifier_(logic)
Mathematical table used in logic
With respect to the result, this example may be arithmetically viewed as modulo 2 binary addition, and as logically equivalent to the exclusive-or (exclusive
Truth_table
Components of a mathematical or logical formula
an inverse σ−1, and t = uσ−1. Both terms are then also said to be equal modulo renaming. In many contexts, the particular variable names in a term don't
Term_(logic)
Algorithm using holographic reduction
problems without such previously known solutions for special cases of satisfiability, vertex cover, and other graph problems. They have received notable
Holographic_algorithm
Geometry problem on tiling by hypercubes
tilings of this special form. In this case, the group of integer translations modulo the translations that preserve the tiling forms an abelian group, and certain
Keller's_conjecture
1969 non-fiction book by G. Spencer-Brown
complementation can be nullary, in which case it denotes a primitive value. Modulo this detail, 2 is a model of the primary algebra. The primary arithmetic
Laws_of_Form
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
Girl/Female
African, Australian, Nigerian
I am Grateful; Gratefulness
Boy/Male
Hindu
Name of Lord Shiva
Surname or Lastname
English
English : variant of Mule.
Boy/Male
Hindu, Indian, Telugu
Lord Shiva; Wearing
Surname or Lastname
English
English : from the Middle English female personal name Mau(l)d, a reduced form of the Norman name Mathilde, Matilda, composed of the Germanic elements maht ‘might’, ‘strength’ + hild ‘strife’, ‘battle’. The learned form Matilda was much less common in the Middle Ages than the vernacular forms Mahalt, Maud and the reduced pet form Till. The name was borne by the daughter of Henry I of England, who disputed the throne of England with her cousin Stephen for a number of years (1137–48). In Germany the popularity of the name in the Middle Ages was augmented by its being borne by a 10th-century saint, wife of Henry the Fowler and mother of Otto the Great.
Girl/Female
Christian & English(British/American/Australian)
Model or Pattern
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Attractive
Boy/Male
Muslim
Model, Example
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Male
Spanish
Spanish form of Latin Theodulus, TEÓDULO means "god-slave."
Female
English
Variant spelling of Middle English Mauld, MOULD means "mighty in battle."
Boy/Male
Muslim
Sample, Model, Paragon
Boy/Male
Arabic, Muslim
Model; Example
Girl/Female
Hindu, Indian, Traditional
Model; Idea
Girl/Female
Arabic, Muslim
Example; Model; Demo
Boy/Male
Egyptian
To model.
Boy/Male
French, German, Teutonic
Rich
Girl/Female
Hindu, Indian, Marathi
Sacred Thread; Mother
Boy/Male
Arabic, Muslim
Sample; Model; Paragon
Boy/Male
Arabic, Assamese, Indian, Muslim
Main; New
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
Girl/Female
Indian
Shining; Brilliant
Girl/Female
Latin
Strong.
Girl/Female
Tamil
Prayer
Girl/Female
Tamil
One who blesses, Blessing
Boy/Male
Celtic
Lives near the yew tree estate.
Boy/Male
Arabic, Hindu, Indian, Muslim
7 Surah of the Quran Begin with the Letters Ha and Mim; Known Only to God; Another Name for Prophet Muhammad
Female
Czechoslovakian
, rich-gift.
Girl/Female
Indian
Light Ray of Moon
Girl/Female
Celtic
Blessed.
Girl/Female
Arabic, Muslim
Sweet-smelling Flower; Among Er Work is a Commentary on Surah Al-baqarah; She is Mentioned by Salahuddin Al-safdi in his Book as One of the Distinguished People of Egypt
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
SATISFIABILITY MODULO-THEORIES
n.
A fixed part of a module. See Module.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
imp. & p. p.
of Moult
n.
A model or measure.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
v. t.
To form into a particular shape; to shape; to model; to fashion.
n.
To model; also, to modulate.
pl.
of Modulus
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.
pl.
of Morula
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
n.
A fixed compensation or equivalent given instead of payment of tithes in kind, expressed in full by the phrase modus decimandi.
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
p. pr. & vb. n.
of Mould
p. pr. & vb. n.
of Moult