A machine program for theorem-proving
Communications of the ACM
Symbolic Model Checking without BDDs
TACAS '99 Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems
Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
HySAT: An efficient proof engine for bounded model checking of hybrid systems
Formal Methods in System Design
Reachability of Uncertain Nonlinear Systems Using a Nonlinear Hybridization
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Verifying Industrial Hybrid Systems with MathSAT
Electronic Notes in Theoretical Computer Science (ENTCS)
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Improving SAT modulo ODE for hybrid systems analysis by combining different enclosure methods
SEFM'11 Proceedings of the 9th international conference on Software engineering and formal methods
δ-complete decision procedures for satisfiability over the reals
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
dReal: an SMT solver for nonlinear theories over the reals
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving ordinary differential equations (ODEs), we provide a seamless integration of safe numeric overapproximation of initial-value problems into a SAT-modulo-theory (SMT) approach to interval-based arithmetic constraint solving. Interval-based safe numeric approximation of ODEs is used as an interval contractor being able to narrow candidate sets in phase space in both temporal directions: post-images of ODEs (i.e., sets of states reachable from a set of initial values) are narrowed based on partial information about the initial values and, vice versa, pre-images are narrowed based on partial knowledge about post-sets.In contrast to the related CLP(F) approach of Hickey and Wittenberg [12], we do (a) support coordinate transformations mitigating the wrapping effect encountered upon iterating interval-based overapproximations of reachable state sets and (b) embed the approach into an SMT framework, thus accelerating the solving process through the algorithmic enhancements of recent SAT solving technology.