Finiteness analyses are compile-time techniques to determine (suucient) conditions for the niteness of relations computed during the bottom-up execution of a logic program. We examine niteness analyses from the perspective of abstract interpretation. However, problems arise when trying to use standard abstract interpretation theory for niteness analysis. They occur because niteness is not an ad...

pto Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (UMR 6074) Université de Rennes 1 – Insa de Rennes et en Automatique – unité de recherche de Rennes Supervisory Control of Discrete or Hybrid Symbolic systems Abstract In this paper we tackle the safety controller synthesis problem for various models ranging from nite transition systems to hybrid sys...

During recent years, it has been shown that a number of problems in matrix theory are NP-hard, including robust nonsingularity, robust stability, robust positive semide"niteness, robust bounded norm, state feedback stabilization with structural and norm constraints, etc. In this paper, we use standard bounds on empirical probabilities as well as recent results from statistical learning theory o...

It is shown that a class of linear, time-invariant, multi-input multi-output plants can be simultaneously stabilized. This class of plants all have the same number of zeros at in"nity, at zero, or both, but no other zeros in the unstable region. If they have zeros at zero or in"nity, then their gain matrices at zero and in"nity also satisfy a positive-de"niteness condition. There is no restrict...

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A nite criss-cross method, based on least{index resolution, is constructed for solving the LCP. In proving nitenes...

A new approach to computing the mixed μ upper bound (ν) is presented. The method exploits the fact that a positive de£nite matrix V (α) becomes singular when the scalar parameter α decreases to a critical value for a given frequency. A two-level optimization strategy is used with a bisection algorithm branching on the de£niteness of V in an outer loop, and a Semi-De£nite Programming (SDP) probl...

State-reduction and the notion of “actuality” are compared to “passage”through time and the notion of “the present”; already in classical relativity the latter give rise to di¢ culties. The solution proposed here is to treat both tense and value-de…niteness as relational properties or “facts as relations”; likewise the notions of change and probability. In both cases “essential” characteristics...

Here, subgroups of = G(Z) are called congruentially conjugate if their images in G(Z=mZ) are conjugate for each m 2 N (where G is a linear algebraic group de…ned over Q). The result (b) is proved in [GS] using respectable mainstream mathematics (…niteness properties of arithmetic groups, due to Borel and Serre). Problem 1 is to …nd a natural and attractive way to do (a); the existing proof is m...

An example of a nitely presented monoid is given that does not satisfy the homo-topical niteness condition FHT, although it satisses both the homological niteness conditions left FP 1 and right FP 1 .tions left FP 1 and right FP 1 .

In this short paper, we prove the niteness of the criss-cross method by showing a certain binary number of bounded digits associated with each iteration increases monotonically. This new proof immediately suggests the possibility of relaxing the pivoting selection in the criss-cross method without sacri cing the niteness.