DPLL(T)
From HandWiki
In computer science, DPLL(T) is a framework for determining the satisfiability of SMT problems. The algorithm extends the original SAT-solving DPLL algorithm with the ability to reason about an arbitrary theory T.[1][2][3] At a high level, the algorithm works by transforming an SMT problem into a SAT formula where atoms are replaced with Boolean variables. The algorithm repeatedly finds a satisfying valuation for the SAT problem, consults a theory solver to check consistency under the domain-specific theory, and then (if a contradiction is found) refines the SAT formula with this information.[4] Many modern SMT solvers, such as Microsoft's Z3 Theorem Prover and CVC4, use DPLL(T) to power their core solving capabilities.[5][6][7]
References
- ↑ Ganzinger, Harald; Hagen, George; Nieuwenhuis, Robert; Oliveras, Albert; Tinelli, Cesare (2004). Alur, Rajeev; Peled, Doron A.. eds (in en). DPLL(T): Fast Decision Procedures. Lecture Notes in Computer Science. 3114. Springer Berlin Heidelberg. 175–188. doi:10.1007/978-3-540-27813-9_14. ISBN 9783540278139.
- ↑ Nieuwenhuis, Robert; Oliveras, Albert; Tinelli, Cesare (2006). "Solving SAT and SAT Modulo Theories: From an Abstract Davis–Putnam–Logemann–Loveland Procedure to DPLL(T)". J. ACM 53 (6): 937–977. doi:10.1145/1217856.1217859. ISSN 0004-5411.
- ↑ Nieuwenhuis, Robert; Oliveras, Albert (2005). Etessami, Kousha; Rajamani, Sriram K.. eds (in en). DPLL(T) with Exhaustive Theory Propagation and Its Application to Difference Logic. Lecture Notes in Computer Science. 3576. Springer Berlin Heidelberg. 321–334. doi:10.1007/11513988_33. ISBN 9783540316862.
- ↑ Reynolds, Andrew (2015). "Satisfiability Modulo Theories and DPLL(T)". http://homepage.divms.uiowa.edu/~ajreynol/pres-dpllt15.pdf.
- ↑ de Moura, Leonardo; Bjørner, Nikolaj (2008). Ramakrishnan, C. R.; Rehof, Jakob. eds (in en). Z3: An Efficient SMT Solver. Lecture Notes in Computer Science. 4963. Springer Berlin Heidelberg. 337–340. doi:10.1007/978-3-540-78800-3_24. ISBN 9783540788003.
- ↑ Liang, Tianyi; Reynolds, Andrew; Tinelli, Cesare; Barrett, Clark; Deters, Morgan (2014). Biere, Armin; Bloem, Roderick. eds (in en). A DPLL(T) Theory Solver for a Theory of Strings and Regular Expressions. Lecture Notes in Computer Science. Cham: Springer International Publishing. 646–662. doi:10.1007/978-3-319-08867-9_43. ISBN 978-3-319-08867-9.
- ↑ Bruttomesso, Roberto; Cimatti, Alessandro; Franzén, Anders; Griggio, Alberto; Sebastiani, Roberto (2008). Gupta, Aarti; Malik, Sharad. eds (in en). The MathSAT 4 SMT Solver. Lecture Notes in Computer Science. 5123. Springer Berlin Heidelberg. 299–303. doi:10.1007/978-3-540-70545-1_28. ISBN 9783540705451.
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