Journal of Computer and System Sciences
Initial experiments in stochastic satisfiability
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Backjumping for quantified Boolean logic satisfiability
Artificial Intelligence
Contingent planning under uncertainty via stochastic satisfiability
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Nonchronological Backtracking in Stochastic Boolean Satisfiability
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
HySAT: An efficient proof engine for bounded model checking of hybrid systems
Formal Methods in System Design
On the stochastic constraint satisfaction framework
Proceedings of the 2007 ACM symposium on Applied computing
Algorithms for stochastic CSPs
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Resolution for stochastic Boolean satisfiability
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Satisfaction meets expectations: computing expected values of probabilistic hybrid systems with SMT
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
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The stochastic satisfiability modulo theories (SSMT) problem is a generalization of the SMT problem on existential and randomized (aka. stochastic) quantification over discrete variables of an SMT formula. This extension permits the concise description of diverse problems combining reasoning under uncertainty with data dependencies. Solving problems with various kinds of uncertainty has been extensively studied in Artificial Intelligence. Famous examples are stochastic satisfiability and stochastic constraint programming. In this paper, we extend the algorithm for SSMT for decidable theories presented in [FHT08] to non-linear arithmetic theories over the reals and integers which are in general undecidable. Therefore, we combine approaches from Constraint Programming, namely the iSAT algorithm tackling mixed Boolean and non-linear arithmetic constraint systems, and from Artificial Intelligence handling existential and randomized quantifiers. Furthermore, we evaluate our novel algorithm and its enhancements on benchmarks from the probabilistic hybrid systems domain.