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 paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.

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...

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 ...