The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Tool-support for the analysis of hybrid systems and models
Proceedings of the conference on Design, automation and test in Europe
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
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
Linear quantifier elimination as an abstract decision procedure
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
SMT-RAT: an SMT-compliant nonlinear real arithmetic toolbox
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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SMT-solving aims at deciding satisfiability for the existential fragment of a first-order theory. A SAT-solver handles the logical part of a given problem and invokes an embedded theory solver to check consistency of theory constraints. For efficiency, the theory solver should be able to work incrementally and generate infeasible subsets. Currently available decision procedures for real algebra - the first-order theory of the reals with addition and multiplication - do not exhibit these features. In this paper we present an adaptation of the virtual substitution method, providing these abilities.