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We investigate the combination of propositional SAT checkers with satisfiability procedures for domain-specific theories such as linear arithmetic, arrays, lists and the combination thereof. Our procedure realizes a lazy approach to satisfiability checking of Boolean constraint formulas by iteratively refining Boolean formulas based on lemmas generated on(More)
We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step(More)
Ground decision procedures for combinations of theories are used in many systems for automated deduction. There are two basic paradigms for combining decision procedures. The Nelson–Oppen method combines decision procedures for disjoint theories by exchanging equality information on the shared variables. In Shostak’s method, the combination of the theory of(More)
In this paper we describe a decision procedure for the core theory of xed-sized bit-vectors with extraction and composition than can readily be integrated into Shostak's procedure for deciding combinations of theories. Inputs to the solver are unquantiied bit-vector equations t = u and the algorithm returns true if t = u is valid in the bit-vector theory,(More)
Automated theorem proving lies at the heart of all tools for formal analysis of software and system descriptions. In formal verification systems such as PVS [10], the deductive capability is explicit and visible to the user, whereas in tools such as test case generators it is hidden and often ad-hoc. Many tools for formal analysis would benefit—both in(More)