We consider proof systems with sequents of the form U for proving validity of a propositional modal calculus formula over a set U of states in a given model Such proof systems usually handle xed point formulae through unfolding thus allowing such formulae to reappear in a proof Tagging is a technique originated by Winskel for annotating xed point formulae with information about the proof states...

A nonlinear generalization of the S-transform known in Gaussian analysis is introduced. It is deened as a nonlinear operator on topolog-ical spaces of entire functions of innnitely many variables with growth of at most second order and nite type restricted to a certain value. This nonlinear S-transform (NLST) has xed points a certain family of which is found and analyzed. In particular, their s...

Most of the existing Digital Signal Processors (DSPs) are optimized for a fast and e cient computation of the Fast Fourier Transform (FFT). However, there are only two oating-point DSPs available, which perform the butter y operation of a FFT in 4 processor cycles, but no xed-point DSP is designed that way. The new 24 bit xed-point DSP DAISY, which is able to execute the butter y in 4 cycles ev...

We describe an encoding of major parts of domain theory and xed-point theory in the Pvs extension of the simply-typed-calculus; these formaliza-tions comprise the encoding of mathematical structures like complete partial orders (domains), domain constructions, the Knaster-Tarski xed-point theorem for mono-tonic functions, and variations of xed-point induction. Altogether, these encodings form a...

Fixed point calculus is about the solution of recursive equations de ̨ned by a monotonic endofunction on a partially ordered set. This tutorial presents the basic theory of ̨xed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also presents the theory and application of Galois connections between partially ordered se...

In this article we present a variant of the basic result of "T. Gnana. Bhaskar and V. Lakshmikanthan, Fixed point theorem in partially ordered metric spaces and applications, Nonlinear Anal. TMA, 65 (2006), 1379–1393." to …nd the coupled …xed points of multivalued mappings without mixed monotone property in cone metric space involving non-normal cones. As applications we prove the existence of ...

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 Steiner tree problem is to nd the tree with minimal Euclidean length spanning a set of xed points in the plane, given the ability to add points (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an eecient method for computing a locally optimal tree with a given topology. The rst systematically inserts S...

We introduce Partitioned Dependency Graphs (PDGs), an abstract framework for the speci cation and evaluation of arbitrarily nested alternating xed points. The generality of PDGs subsumes that of similarly proposed models of nested xed-point computation such as Boolean graphs, Boolean equation systems, and the propositional modal mu-calculus. Our main result is an e cient local algorithm for eva...

Nonstandard methods are used to obtain results about sets formed by simple dense canals in the plane. The …rst main result considers internal regions V that contain no standard points and have the property that st(V ) does not disconnect the plane and are bounded by simple closed curves that have small intersection with st(V ): We show that such sets must be somewhat one-dimensional in the sens...