77,407 research outputs found

    New results on rewrite-based satisfiability procedures

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    Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

    Quantifier-Free Interpolation of a Theory of Arrays

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    The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

    Instantiation of SMT problems modulo Integers

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    Many decision procedures for SMT problems rely more or less implicitly on an instantiation of the axioms of the theories under consideration, and differ by making use of the additional properties of each theory, in order to increase efficiency. We present a new technique for devising complete instantiation schemes on SMT problems over a combination of linear arithmetic with another theory T. The method consists in first instantiating the arithmetic part of the formula, and then getting rid of the remaining variables in the problem by using an instantiation strategy which is complete for T. We provide examples evidencing that not only is this technique generic (in the sense that it applies to a wide range of theories) but it is also efficient, even compared to state-of-the-art instantiation schemes for specific theories.Comment: Research report, long version of our AISC 2010 pape

    A simple abstraction of arrays and maps by program translation

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    We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

    The SST-1M camera for the Cherenkov Telescope Array

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    The prototype camera of the single-mirror Small Size Telescopes (SST-1M) proposed for the Cherenkov Telescope Array (CTA) project has been designed to be very compact and to deliver high performance over thirty years of operation. The camera is composed of an hexagonal photo-detection plane made of custom designed large area hexagonal silicon photomultipliers and a high throughput, highly configurable, fully digital readout and trigger system (DigiCam). The camera will be installed on the telescope structure at the H. Niewodnicza{\'n}ski institute of Nuclear Physics in Krakow in fall 2015. In this contribution, we review the steps that led to the development of the innovative photo-detection plane and readout electronics, and we describe the test and calibration strategy adopted.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.05894; Full consortium author list at http://cta-observatory.or

    On Deciding Local Theory Extensions via E-matching

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    Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

    Planning for sustainable development of energy infrastructure: fast – fast simulation tool

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    Energy management has significant impact on planning within local or regional scale. The consequences of the implementation of large-scale renewable energy source involves multifaceted analyses, evaluation of environmental impacts, and the assessment of the scale of limitations or exclusions imposed on potential urbanized structures and arable land. The process of site designation has to acknowledge environmental transformations by inclusion of several key issues, e.g. emissions, hazards for nature and/or inhabitants of urbanized zones, to name the most significant. The parameters of potential development of energy-related infrastructure of facility acquire its local properties – the generic development data require adjustment, which is site specific or area specific. FAST (Fast Simulation Tool) is a simple IT tool aimed at supporting sustainable planning on local or regional level in reference to regional or district scale energy management (among other issues). In its current stage, it is utilized – as a work in progress – in the assessment of wind farm structures located within the area of Poznan agglomeration. This paper discusses the implementation of FAST and its application in two conflicting areas around the agglomeration of Poznan
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