The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
The software model checker Blast: Applications to software engineering
International Journal on Software Tools for Technology Transfer (STTT)
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
A combination method for generating interpolants
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Generating non-linear interpolants by semidefinite programming
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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An increasing number of applications in particular in the verification area leverages Craig interpolation. Craig interpolants (CIs) can be computed for many different theories such as: propositional logic, linear inequalities over the reals, and the combination of the preceding theories with uninterpreted function symbols. To the best of our knowledge all previous tools that provide CIs are addressing decidable theories. With this paper we make Craig interpolation available for an in general undecidable theory that contains Boolean combinations of linear and non-linear constraints including transcendental functions like sin(ċ) and cos(ċ). Such formulae arise e.g. during the verification of hybrid systems. We show how the construction rules for CIs can be extended to handle non-linear constraints. To do so, an existing SMT solver based on a close integration of SAT and Interval Constraint Propagation is enhanced to construct CIs on the basis of proof trees. We provide first experimental results demonstrating the usefulness of our approach: With the help of Craig interpolation we succeed in proving safety in cases where the basic solver could not provide a complete answer. Furthermore, we point out the (heuristic) decisions we made to obtain suitable CIs and discuss further possibilities to increase the flexibility of the CI construction.