Finite state automata with counters are useful for modeling systems with discrete parameters. The calculation of state invariants is an important tool in the analysis of such systems. Previous authors have presented techniques for the calculation of state invariants based on their approximation by convex polyhedra or periodic sets. In this paper we present a new method for the calculation of in...

In this article, we present general properties of xed-point groups of the automorphisms of nite groups. Speci cally, we determine the form of xed-point groups and partition Aut(G) according to the number of xed points possessed by each automorphism. A function θ records the size of each partitioning set; we nd properties for θ in general and develop formulae for θ with respect to certain classe...

The breakdown point behavior of M-estimators in linear models with xed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at xed designs is quite diierent from that at designs which can be corrupted by outliers|the situation prevailing in the literature. For xed designs, the breakdown points of robust M-estimators (those with bounded ...

In the companion paper 7] a grouping strategy with a rm geometrical underpinning and without the problem of combinatorics is proposed. It is based on the exploitation of structures that remain xed under the transformations that relate corresponding contour segments in regular patterns. In this paper we present a solution for the complementary task of extracting these xed structures in an eecien...

We develop a model-checking algorithm for a logic that permits propositions to be deened using greatest and least xed points of mutually recursive systems of equations. This logic is as expressive as the alternation-free fragment of the modal mu-calculus identiied by Emerson and Lei, and it may therefore be used to encode a number of temporal logics and behavioral preorders. Our algorithm deter...

A generic four-dimensional model representing the nonlin-ear betatronic oscillations of a single particle in a magnetic lattice for hadrons is considered. The classiication of the diierent resonances is given and the computation of the corresponding normal form invariant is outlined. The analysis of the interpolating Hamiltonian of the resonant normal form allows to determine xed points, xed cu...

Constructive type theory as conceived by Per Martin-LL of has a very rich type system, but partial functions cannot be typed. This also makes it impossible to directly write recursive programs. In this paper a constructive type theory Red is deened which includes a partial type constructor A; objects in the type A may diverge, but if they converge, they must be members of A. A xed point typing ...

Bayesian D-optimal designs supported on a xed number of points were found by Dette and Wong (1998) for estimating parameters in a polynomial model when the error variance depends exponentially on the explanatory variable. This work provides optimal designs under a broader class of error variance structures and investigates the robustness properties of these designs to model and prior distributi...

The eeect on p-mode frequencies of changing the near-surface structure of solar models is investigated. As is well known, changes connned to the near-surface region have little eeect on the low-frequency p modes: this is as one would expect from a simple asymp-totic description which shows that these modes have upper turning points located well beneath the photosphere. However, some examples of...

We study the problem of the maximum number of unit distances among n points in the plane under the additional restriction that we count only those unit distances that occur in a xed set of k directions taking the maximum over all sets of n points and all sets of k directions We prove that for xed k and su ciently large n n k the extremal sets are essentially sections of lattices bounded by edge...