Apostolos Syropoulos

Mathematics of Multisets

This paper is an attempt to summarize the basic elements of the multiset theory. We begin by describing multisets and the operations between them, then we present hybrid sets and their operations. We continue with a categorical approach to multisets,and then we present fuzzy multisets and their operations. Finally, we present partially ordered multisets.

A Distributed Simulation of Transition P Systems

P systems is a new model of computation, inspired by natural processes, that has a distributive nature. By exploring this distributive nature of P systems, we have built a purely distributive simulation of P systems. The simulation, whose implementation is described here, was programmed in the Java programming language and makes heavy use of its Remote Method Invocation protocol. The class of P systems that the simulator can accept is a subset of the NOP2(coo, tar) family of systems, which have the computational power of Turing machines. The paper concludes with some remarks concerning the usefulness of the simulation. In addition, there is a brief discussion of some ideas that can be used in the formulation of a foundation of distributive computing.

Fuzzy sets and fuzzy relational structures as Chu spaces

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

YET ANOTHER FUZZY MODEL FOR LINEAR LOGIC

The construction of a new categorical fuzzy model for linear logic is presented. The construction is based on a general poset-valued model. Since the resulting categories are not identical to existing categories of all fuzzy sets, we investigate the relationship between the two categories. We conclude with very brief comments regarding the usefulness of this work.

Categorical relationships between Goguen sets and “two-sided” categorical models of linear logic

Abstract The relationships between “two-sided” categorical models of linear logic and Goguen sets is investigated. In particular, we show that only certain Goguen sets can be represented as Chu spaces, while it is possible to represent any Goguen set as a Dialectica space. In addition, we discuss the benefits of these representations.

New technologies for rapid development of Web orientated database applications

Many new Internet technologies are available to Web programmers. Using these technologies it is now easy to develop dynamic Web based applications that use databases. We describe some of these new technologies and we briefly present two examples showing how we can use these technologies in real world applications.

Literate programming and the “Spaniel“ method

Software has to be well structured and well documented in order to be reusable and maintainable. Literate programs have both properties. Unfortunately, even today many programmers write program without proper documentation. We propose a technique by which one can relatively easily transform a well structured program into a literate one. We exemplify the technique by means of an example and we conclude with the presentation of some related work and ideas.

A note on type checking linear functional languages

A linear functional language is based on a linear λ-calculus. Any linear functional program must observe linearity and it has to be type correct. Type correctness can be ensured by means of a type-checking system. A type checker for a linear functional language is essentially a type-checker for an ordinary functional language, modified to properly handle the modality ofcourse.

Bottom in the imperative world

Bottom is used in functional programming languages to denote abnormal situations. We propose the incorporation of this value in any existing imperative language. We show how this can be done and finally what are the benefits of the bottom incorporation in any imperative language.Covariant deep subtyping has always been viewed as a way to narrow the range of a component in subtypes. In this paper, however, we will see covariant deep subtyping in a new light---a way to clarify a vague but fixed range of a component in subclasses. We will also examine such concepts as class substitution, generic calss by BETA/Cluster, and a number of theoretic approaches in relation to covariant deep subtyping.

A (Basis for a) Philosophy of a Theory of Fuzzy Computation

Abstract Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, an attempt is made to formulate a basis for a philosophy of a theory of fuzzy computation.