6,388 research outputs found

    A Faithful Semantics for Generalised Symbolic Trajectory Evaluation

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    Generalised Symbolic Trajectory Evaluation (GSTE) is a high-capacity formal verification technique for hardware. GSTE uses abstraction, meaning that details of the circuit behaviour are removed from the circuit model. A semantics for GSTE can be used to predict and understand why certain circuit properties can or cannot be proven by GSTE. Several semantics have been described for GSTE. These semantics, however, are not faithful to the proving power of GSTE-algorithms, that is, the GSTE-algorithms are incomplete with respect to the semantics. The abstraction used in GSTE makes it hard to understand why a specific property can, or cannot, be proven by GSTE. The semantics mentioned above cannot help the user in doing so. The contribution of this paper is a faithful semantics for GSTE. That is, we give a simple formal theory that deems a property to be true if-and-only-if the property can be proven by a GSTE-model checker. We prove that the GSTE algorithm is sound and complete with respect to this semantics

    Stable foliations near a traveling front for reaction diffusion systems

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    We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the differential operator obtained by linearization at the front touches the imaginary axis. In spaces with exponential weights, one can shift the spectrum to the left. We study the nonlinear equation on the intersection of the unweighted and weighted spaces. Small translations of the front form a center unstable manifold. For each small translation we prove the existence of a stable manifold containing the translated front and show that the stable manifolds foliate a small ball centered at the front

    Global wave-front sets of Banach, Fr{\'e}chet and Modulation space types, and pseudo-differential operators

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    We introduce global wave-front sets WFB(f)\operatorname{WF}_{{\mathcal B}} (f), fS(Rd)f\in {\mathscr S}^\prime(\textbf{R}^d), with respect to suitable Banach or Fr\'echet spaces B{\mathcal B}. An important special case is given by the modulation spaces B=M(ω,B){\mathcal B}=M(\omega,\mathscr B), where ω\omega is an appropriate weight function and B\mathscr B is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to WFB(f)\operatorname{WF}_{{\mathcal B}} (f). In particular, we prove that micro locality and microellipticity hold for a class of globally defined pseudo-differential operators Opt(a)\operatorname{Op}_t(a), acting continuously on the involved spaces.Comment: 51 pages, mistakes and typos correction, reorganized material

    A Static Analyzer for Large Safety-Critical Software

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    We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)
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