Foundations of programming languages
Foundations of programming languages
Term rewriting and all that
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Strategies for combining decision procedures
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Combined satisfiability modulo parametric theories
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Splitting on demand in SAT modulo theories
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Combining data structures with nonstably infinite theories using many-sorted logic
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Theorem Proving for Verification (Invited Tutorial)
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Instance-Based Selection of Policies for SAT Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Ground Interpolation for Combined Theories
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Formal verification of a modern SAT solver by shallow embedding into Isabelle/HOL
Theoretical Computer Science
Cutting to the Chase solving linear integer arithmetic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
CDCL-based abstract state transition system for coherent logic
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Quantifier instantiation techniques for finite model finding in SMT
CADE'13 Proceedings of the 24th international conference on Automated Deduction
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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We offer a transition system representing a high-level but detailed architecture for SMT solvers that combine a propositional SAT engine with solvers for multiple disjoint theories. The system captures succintly and accurately all the major aspects of the solver's global operation: boolean search with across-the-board backjumping, communication of theory-specific facts and equalities between shared variables, and cooperative conflict analysis. Provably correct and prudently underspecified, our system is a usable ground for high-quality implementations of comprehensive SMT solvers.