The CLP( R ) language and system
ACM Transactions on Programming Languages and Systems (TOPLAS)
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Solving linear arithmetic constraints for user interface applications
Proceedings of the 10th annual ACM symposium on User interface software and technology
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Backtracking algorithms for disjunctions of temporal constraints
Artificial Intelligence
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Bounded Model Checking for Timed Systems
FORTE '02 Proceedings of the 22nd IFIP WG 6.1 International Conference Houston on Formal Techniques for Networked and Distributed Systems
On Solving Presburger and Linear Arithmetic with SAT
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
The Quest for Efficient Boolean Satisfiability Solvers
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
SAT-Based Procedures for Temporal Reasoning
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
RTL-Datapath Verification using Integer Linear Programming
ASP-DAC '02 Proceedings of the 2002 Asia and South Pacific Design Automation Conference
An efficient finite-domain constraint solver for circuits
Proceedings of the 41st annual Design Automation Conference
AI Communications - CASC
Continuous time in a SAT-based planner
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
A SAT-based decision procedure for the boolean combination of difference constraints
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
An incremental and layered procedure for the satisfiability of linear arithmetic logic
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Processes and continuous change in a SAT-based planner
Artificial Intelligence
Rewrite-Based Decision Procedures
Electronic Notes in Theoretical Computer Science (ENTCS)
From KSAT to Delayed Theory Combination: Exploiting DPLL Outside the SAT Domain
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Encoding Queues in Satisfiability Modulo Theories Based Bounded Model Checking
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Stable models and difference logic
Annals of Mathematics and Artificial Intelligence
Computing Stable Models via Reductions to Difference Logic
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
SAT encodings of state-space reachability problems in numeric domains
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Processes and continuous change in a SAT-based planner
Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
An extension of the Davis-Putnam procedure and its application to preprocessing in SMT
Proceedings of the 7th International Workshop on Satisfiability Modulo Theories
Boolean abstraction for temporal logic satisfiability
CAV'07 Proceedings of the 19th international conference on Computer aided verification
A lazy and layered SMT(BV) solver for hard industrial verification problems
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Guiding the correction of parameterized specifications
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Efficient interpolant generation in satisfiability modulo theories
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
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
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Fully symbolic model checking for timed automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Retrenchment, and the generation of fault trees for static, dynamic and cyclic systems
SAFECOMP'06 Proceedings of the 25th international conference on Computer Safety, Reliability, and Security
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Building efficient decision procedures on top of SAT solvers
SFM'06 Proceedings of the 6th international conference on Formal Methods for the Design of Computer, Communication, and Software Systems
Solving disjunctive temporal problems with preferences using maximum satisfiability
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
The strategy challenge in SMT solving
Automated Reasoning and Mathematics
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Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard real-world problems (e.g., model-checking, circuit testing, propositional planning) by encoding into SAT. However, a purely Boolean representation is not expressive enough for many other real-world applications, including the verification of timed and hybrid systems, of proof obligations in software, and of circuit design at RTL level. These problems can be naturally modeled as satisfiability in linear arithmetic logic (LAL), that is, the Boolean combination of propositional variables and linear constraints over numerical variables. In this paper we present MathSAT, a new, SAT-based decision procedure for LAL, based on the (known approach) of integrating a state-of-the-art SAT solver with a dedicated mathematical solver for LAL. We improve MathSAT in two different directions. First, the top驴level line procedure is enhanced and now features a tighter integration between the Boolean search and the mathematical solver. In particular, we allow for theory-driven backjumping and learning, and theory-driven deduction; we use static learning in order to reduce the number of Boolean models that are mathematically inconsistent; we exploit problem clustering in order to partition mathematical reasoning; and we define a stack-based interface that allows us to implement mathematical reasoning in an incremental and backtrackable way. Second, the mathematical solver is based on layering; that is, the consistency of (partial) assignments is checked in theories of increasing strength (equality and uninterpreted functions, linear arithmetic over the reals, linear arithmetic over the integers). For each of these layers, a dedicated (sub)solver is used. Cheaper solvers are called first, and detection of inconsistency makes call of the subsequent solvers superfluous. We provide a through experimental evaluation of our approach, by taking into account a large set of previously proposed benchmarks. We first investigate the relative benefits and drawbacks of each proposed technique by comparison with respect to a reference option setting. We then demonstrate the global effectiveness of our approach by a comparison with several state-of-the-art decision procedures. We show that the behavior of MathSAT is often superior to its competitors, both on LAL and in the subclass of difference logic.