DPLL(T)

E904156

SMT solving framework algorithmic framework decision procedure framework

DPLL(T) is a framework that extends the classic DPLL SAT-solving algorithm with theory solvers to efficiently decide satisfiability modulo background theories such as arithmetic, arrays, or bit-vectors.

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All labels observed (3)

Label	Occurrences
DPLL(T) canonical	3
DPLL(T) framework	1
DPLL(T) style solving engine	1

How this entity was disambiguated

This entity first appeared as the object of triple T11090175 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: DPLL(T)
Context triple: [Satisfiability Modulo Theories, typicalArchitecture, DPLL(T)]

A. Satisfiability Modulo Theories (SMT)
Satisfiability Modulo Theories (SMT) is a framework in computer science and mathematical logic for deciding the satisfiability of logical formulas with respect to background theories such as arithmetic, bit-vectors, arrays, and data types, widely used in verification, synthesis, and automated reasoning.
B. Z3: An Efficient SMT Solver
Z3: An Efficient SMT Solver is a high-performance satisfiability modulo theories (SMT) solver widely used in program verification, formal methods, and automated reasoning.
C. CDCL SAT solver
A CDCL SAT solver is an advanced algorithm for solving Boolean satisfiability problems that extends the classic DPLL approach with conflict-driven clause learning and non-chronological backtracking to greatly improve efficiency on large, complex instances.
D. Davis–Putnam algorithm
The Davis–Putnam algorithm is a pioneering procedure in automated theorem proving and propositional logic satisfiability that laid foundational groundwork for modern SAT solvers.
E. Vampire automated theorem prover
Vampire automated theorem prover is a high-performance first-order logic reasoning system widely used in automated deduction and formal verification research.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: DPLL(T)
Target entity description: DPLL(T) is a framework that extends the classic DPLL SAT-solving algorithm with theory solvers to efficiently decide satisfiability modulo background theories such as arithmetic, arrays, or bit-vectors.

A. Satisfiability Modulo Theories (SMT)
Satisfiability Modulo Theories (SMT) is a framework in computer science and mathematical logic for deciding the satisfiability of logical formulas with respect to background theories such as arithmetic, bit-vectors, arrays, and data types, widely used in verification, synthesis, and automated reasoning.
B. Z3: An Efficient SMT Solver
Z3: An Efficient SMT Solver is a high-performance satisfiability modulo theories (SMT) solver widely used in program verification, formal methods, and automated reasoning.
C. CDCL SAT solver
A CDCL SAT solver is an advanced algorithm for solving Boolean satisfiability problems that extends the classic DPLL approach with conflict-driven clause learning and non-chronological backtracking to greatly improve efficiency on large, complex instances.
D. Davis–Putnam algorithm
The Davis–Putnam algorithm is a pioneering procedure in automated theorem proving and propositional logic satisfiability that laid foundational groundwork for modern SAT solvers.
E. Vampire automated theorem prover
Vampire automated theorem prover is a high-performance first-order logic reasoning system widely used in automated deduction and formal verification research.
F. None of above. chosen

Statements (45)

Predicate	Object
instanceOf	SMT solving framework ⓘ algorithmic framework ⓘ decision procedure framework ⓘ
abbreviationOf	Davis–Putnam–Logemann–Loveland with Theories ⓘ linked to: Shostak decision procedure in automated reasoning
basedOn	DPLL ⓘ linked to: DPLL algorithm
checks	theory consistency of partial assignments ⓘ
combines	Boolean reasoning ⓘ theory reasoning ⓘ
communicatesVia	interface between SAT solver and theory solver ⓘ
designedFor	Satisfiability Modulo Theories ⓘ linked to: Satisfiability Modulo Theories (SMT)
enables	incremental theory reasoning ⓘ lazy theory instantiation ⓘ
extends	DPLL SAT-solving algorithm ⓘ linked to: DPLL algorithm
goal	efficient decision procedures for SMT problems ⓘ
hasComponent	Boolean search engine ⓘ clause learning ⓘ conflict analysis ⓘ theory consistency checking ⓘ theory propagation ⓘ
improvesOn	pure SAT-based decision procedures for rich theories ⓘ
influenced	modern SMT solver architectures ⓘ
operatesOn	Boolean abstraction of theory atoms ⓘ
originField	automated reasoning ⓘ formal methods ⓘ
relatedTo	CDCL ⓘ Nelson–Oppen combination method ⓘ
requires	theory solver for each background theory ⓘ
supports	arithmetic theories ⓘ arrays ⓘ background theories ⓘ bit-vectors ⓘ combinations of theories ⓘ linear arithmetic ⓘ uninterpreted functions ⓘ
typicalImplementationInvolves	backjumping ⓘ conflict-driven clause learning ⓘ unit propagation ⓘ
usedIn	SMT-LIB compliant solvers ⓘ Satisfiability Modulo Theories solvers ⓘ linked to: SMT solvers hardware verification ⓘ model checking ⓘ program analysis ⓘ software verification ⓘ
uses	SAT solver ⓘ theory solver ⓘ