A Faithful Semantics for Generalised Symbolic Trajectory Evaluation

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

Performance analysis of a message-oriented knowledge-base

First-order Horn logic is a useful formalism to design knowledge-based systems. When implemented on a sequential von Neumann computer, the main limitation of such systems is performance. We present a message-driven model for function-free Horn logic, where the knowledge base is represented as a network of logical processing elements communicating with one another exclusively through messages. The lack of centralized control and centralized memory makes this model suitable to implementation on a highly-parallel asynchronous computer architecture.The primary contribution of this paper is a performance analysis of this message-driven system and a comparison with a sequential resolution scheme using backtracking. For both approaches, closed form expressions for the performance results are derived and compared

Stable foliations near a traveling front for reaction diffusion systems

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

A data-driven model for parallel interpretation of logic programms [sic]

The main objective of this paper is to present a model of computation which permits logic programs to be executed on a highly-parallel computer architecture. It demonstrates how logic programs may be converted into collections of dataflow graphs in which resolution is viewed as a process of finding matches between certain graph templates and portions of the dataflow graphs. This graph fitting process is carried out by tokens propogating asynchronously through the dataflow graph; thus computation is entirely data-driven, without the need for any centralized control. It is shown that at the implementation level the proposed model is very similar to a general dataflow system and hence a dataflow architecture could easily be extended to support the proposed model

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

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

A Static Analyzer for Large Safety-Critical Software

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)