Decision procedures for decidable logics and logical theories have proven to be useful tools in verification. This paper describes the CVC ("Cooperating Validity Checker") decision procedure. CVC implements a framework for combining subsidiary decision procedures for certain logical theories into a decision procedure for the theories' union. Subsidiary decision procedures for theories of arrays, inductive datatypes, and linear real arithmetic are currently implemented. Other notable features of CVC are the incorporation of the high-performance Cha solver for propositional reasoning, and the ability to produce independently checkable proofs for valid formulas.

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We outline an approach to use ordering-based theorem-proving strategies as satisfiability procedures for certain decidable theories. We report on experiments with synthetic benchmarks in the theory of arrays with extensionality, showing that a theorem prover -- the E system -- compares favorably with the state-of-the-art validity checker CVC.

Abstract. Despite many advances, today’s software model checkers and extended static checkers still do not scale well to large code bases, when verifying properties that depend on complex interprocedural flow of data. An obvious approach to improve performance is to exploit software structure. Although a tremendous amount of work has been done on exploiting structure at various levels of granularity, the fine-grained shared structure among multiple verification conditions has been largely ignored. In this paper, we formalize the notion of shared structure among verification conditions, propose a novel and efficient approach to exploit this sharing, and provide experimental results that this approach can significantly improve the performance of verification, even on pathand context-sensitive and dataflow-intensive properties. 1

Satisfiability Modulo Theories (SMT) solvers are large and complicated pieces of code. As a result, ensuring their correctness is challenging. In this paper, we discuss a technique for ensuring soundness by producing and checking proofs. We give details of our implementation using CVC3 and HOL Light and provide initial results from our effort to certify the SMT-LIB benchmarks. 1

Z3 [3] is a state-of-the-art Satisfiability Modulo Theories (SMT) solver freely available from Microsoft Research. It solves the decision problem for quantifier-free formulas with respect to combinations of theories, such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is used in various software analysis and test-case generation projects at Microsoft Research and elsewhere. The requirements from the user-base range from establishing validity, dually unsatisfiability, of firstorder formulas; to identify invalid, dually satisfiable, formulas. In both cases, there is often a need for more than just a yes/no answer from the prover. A model can exhibit why an invalid formula is not provable, and a proof-object can certify the validity of a formula. This paper describes the proof-producing internals of Z3. We also briefly introduce the model-producing facilities. We emphasize two features that can be of general interest: (1) we introduce a notion of implicit quotation to avoid introducing auxiliary variables, it simplifies the creation of proof objects considerably; (2) we produce natural deduction style proofs to facilitate modular proof re-construction.

The standard input format for Satisfiability Modulo Theories (SMT) solvers has now reached its second version and integrates many of the features useful for users to interact with their favourite SMT solver. However, although many SMT solvers do output proofs, no standardised proof format exists. We, here, propose for discussion at the PxTP Workshop a generic proof format in the SMT-LIB philosophy that is flexible enough to be easily recast for any SMT solver. The format is configurable so that the proof can be provided by the solver at the desired level of detail. 1

Over the past decade, since Java was first introduced and integrated into the Netscape web browser, several intermediate representations have been developed that might be potentially used for mobile code applications. This paper examines the requirements for a mobile code representation, presents several examples of stack-based, tree-oriented, and proof-annotating mobile code representations, and evaluates each of these representations according to the requirements. Povzetek: Članek podaja pregled mobilnih kod. 1

Existing automated provers and proof assistants are complementary, to the point that their cooperative integration would benefit all efforts in automating reasoning. Indeed, a number of specialized tools incorporating such integration have been built. The issue is, however, wider, as we can envisage cooperation among various automated provers as well as among various proof assistants. This workshop brings together practitioners and researchers who have experimented with knowledge exchange among tools supporting automated reasoning. Organizers: Piotr Rudnicki, Geoff Sutcliffe