The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

Low-degree tests at large distances

We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between soundness and the number of queries. In particular, we show that functions with small Gowers uniformity norms behave ``randomly'' with respect to hypergraph linearity tests. A central step in our analysis of quadraticity tests is the proof of an inverse theorem for the third Gowers uniformity norm of boolean functions. The last result has also a coding theory application. It is possible to estimate efficiently the distance from the second-order Reed-Muller code on inputs lying far beyond its list-decoding radius

Transformation Techniques for OCL Constraints

Constraints play a key role in the definition of conceptual schemas. In the UML, constraints are usually specified by means of invariants written in the OCL. However, due to the high expressiveness of the OCL, the designer has different syntactic alternatives to express each constraint. The techniques presented in this paper assist the designer during the definition of the constraints by means of generating equivalent alternatives for the initially defined ones. Moreover, in the context of the MDA, transformations between these different alternatives are required as part of the PIM-to-PIM, PIM-to-PSM or PIM-to-code transformations of the original conceptual schema

Automation In The Design Of Asynchronous Sequential Circuits

Sequential switching circuits are commonly classified as being either synchronous or asynchronous. Clock pulses synchronize the operations of the synchronous circuit. The operation of an asynchronous circuit is usually assumed to be independent of such clocks. The operating speed of an asynchronous circuit is thus limited only by basic device speed. One disadvantage of asynchronous circuit design has been the complexity of the synthesis procedures for large circuits

Controller synthesis with very simplified linear constraints in PN model

This paper addresses the problem of forbidden states for safe Petri net modeling discrete event systems. We present an efficient method to construct a controller. A set of linear constraints allow forbidding the reachability of specific states. The number of these so-called forbidden states and consequently the number of constraints are large and lead to a large number of control places. A systematic method for constructing very simplified controller is offered. By using a method based on Petri nets partial invariants, maximal permissive controllers are determined.Comment: Dependable Control of discrete Systems, Bari : Italie (2009