Abstract. Craig interpolation is an active research topic and has become a powerful technique in verification. We present SMTInterpol, an interpolating SMT solver for the quantifier free fragment of the combination of the theory of uninterpreted functions and the theory of linear arithmetic over integers and reals. A core feature of SMTInterpol is the computation of an inductive sequence of interpolants from a single proof of unsatisfiability. SMTInterpol is SMTLIB 2 compliant and available under an open source software license.

Abstract. Identifying the cause of an error is often the most timeconsuming part in program debugging. Fault localization techniques can help to automate this task. Particularly promising are static proof-based techniques that rely on an encoding of error traces into trace formulas. By identifying irrelevant portions of the trace formula, the possible causes of the error can be isolated. One limitation of these approaches is that they do not take into account the control flow of the program and therefore miss common causes of errors, such as faulty branching conditions. This limitation is inherent to the way the error traces are encoded. In this paper, we present a new flow-sensitive encoding of error traces into trace formulas. The new encoding enables proof-based techniques to identify irrelevant conditional choices in an error trace and to include a justification for the truth value of branching conditions that are relevant for the localized cause of an error. We apply our new encoding to the fault localization technique based on error invariants and show that it produces more meaningful error explanations than previous approaches.

Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it transform the proof tree before extracting interpolants. Our scheme works for the combination of uninterpreted functions and linear arithmetic but is extendable to other theories. The scheme is implemented in the interpolating SMT solver SMTInterpol.

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The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and extensionality axioms originally proposed by McCarthy. Various filters are used to limit the number of axiom instantiations while preserving completeness. We present an algorithm that lazily instantiates lemmas based on weak equivalence classes. These lemmas are easier to interpolate as they only contain existing terms. We formally define weak equivalence and show correctness of the resulting decision procedure.