We present an axiomatization of Conway theories which yields, as a corollary, a very concise axiomatization of iteration theories satisfying the functorial implication for base morphisms. It has been shown that most fixed point operations in computer science share the same equational properties. These equational properties are captured by the notion of iteration theories [1, 3]. Several axiomat...

Given a positive integer k and a directed graph with a cost on each edge, the k-length negative cost cycle (kLNCC ) problem is to determine whether there exists a negative cost cycle with at least k edges, and the fixed-point k-length negative cost cycle trail (FPkLNCCT) problem is to determine whether there exists a negative trail enrouting a given vertex (as the fixed point) and containing on...

We present two modal typing systems with the approximation modality, which has been proposed by the author to capture selfreferences involved in computer programs and their speci cations. The systems are based on the simple and the F-semantics of types, respectively, and correspond to the same modal logic, which is considered the intuitionistic version of the logic of provability. We also show ...

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

Banach’s fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach’s theorem limited. We explore how generally we can apply Banach’s fixed point theorem to ...

Q-reducibility is a natural generalization of many-one reducibility (m-reducibility): if A ≤m B via a computable function f(x), then A ≤Q B via the computable function g(x) such that Wg(x) = {f(x)}. Also this reducibility is connected with enumeration reducibility (e-reducibility) as follows: if A ≤Q B via a computable function g(x), then ω −A ≤e ω −B via the c. e. set W = {〈x, 2y〉 | x ∈ ω, y ∈...