A Model-Constructing Satisfiability Calculus

We present a new calculus where recent model-based decision procedures and techniques can be justified and combined with the standard DPLLT approach to satisfiability modulo theories. The new calculus generalizes the ideas found in CDCL-style propositional SAT solvers to the first-order setting.

[1]  Toby Walsh,et al.  Handbook of satisfiability , 2009 .

[2]  Amit Goel,et al.  Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL , 2007, FroCoS.

[3]  Cesare Tinelli,et al.  Splitting on Demand in SAT Modulo Theories , 2006, LPAR.

[4]  P. Smokowski,et al.  Conflict Resolution , 1989, International Conference on Principles and Practice of Constraint Programming.

[5]  Michela Milano.  Principles and Practice of Constraint Programming , 2012, Lecture Notes in Computer Science.

[6]  Kenneth L. McMillan,et al.  Generalizing DPLL to Richer Logics , 2009, CAV.

[7]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[8]  Armin Biere,et al.  Lemmas on demand for the extensional theory of arrays , 2008, SMT '08/BPR '08.

[9]  Scott Cotton.  Natural Domain SMT: A Preliminary Assessment , 2010, FORMATS.

[10]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[11]  Nikolaj Bjørner,et al.  Model-based Theory Combination , 2008, SMT@CAV.

[12]  Nikolaj Bjørner,et al.  Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings , 2011, CADE.

[13]  Sharad Malik,et al.  Boolean satisfiability from theoretical hardness to practical success , 2009, Commun. ACM.

[14]  Leonardo Mendonça de Moura,et al.  Cutting to the Chase , 2011, Journal of Automated Reasoning.

[15]  Cesare Tinelli,et al.  Satisfiability Modulo Theories , 2021, Handbook of Satisfiability.

[16]  Daniel Kroening,et al.  Deciding floating-point logic with systematic abstraction , 2012, 2012 Formal Methods in Computer-Aided Design (FMCAD).

[17]  Joao Marques-Silva,et al.  GRASP-A new search algorithm for satisfiability , 1996, Proceedings of International Conference on Computer Aided Design.

[18]  Leonardo Mendonça de Moura,et al.  Solving non-linear arithmetic , 2012, ACCA.

[19]  Roberto Rossi,et al.  Synthesizing Filtering Algorithms for Global Chance-Constraints , 2009, CP.

[20]  Cesare Tinelli,et al.  Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.

[21]  Jirí Srba,et al.  Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets , 2008, FORMATS.

[22]  Strategic Cad Labs.  Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL , 2007 .

[23]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).