Session Type Isomorphisms

There has been a considerable amount of work on retrieving functions in function libraries using their type as search key. The availability of rich component specifications, in the form of behavioral types, enables similar queries where one can search a component library using the behavioral type of a component as the search key. Just like for function libraries, however, component libraries will contain components whose type differs from the searched one in the order of messages or in the position of the branching points. Thus, it makes sense to also look for those components whose type is different from, but isomorphic to, the searched one. In this article we give semantic and axiomatic characterizations of isomorphic session types. The theory of session type isomorphisms turns out to be subtle. In part this is due to the fact that it relies on a non-standard notion of equivalence between processes. In addition, we do not know whether the axiomatization is complete. It is known that the isomorphisms for arrow, product and sum types are not finitely axiomatisable, but it is not clear yet whether this negative results holds also for the family of types we consider in this work.Comment: In Proceedings PLACES 2014, arXiv:1406.331

A Note on Idempotent Monomial Clones : Two is Strong; One is Weak (Developments of Language, Logic, Algebraic system and Computer Science)

Clones of polynomials are considered over Galois field GF(k). In particular, the class of clones generated by 2-variable idempotent polynomials is the target of our study. Our results include that the clone generated by x^{2}y^{k-2} is the largest among all such clones and the clone generated by xy^{k-1} is the smallest among all such clones. Hence, observing the exponent of one variable, two is strong and one is weak

Measuring linearity of connected configurations of a finite number of 2D and 3D curves

We define a new linearity measure for a wide class of objects consisting of a set of of curves, in both 2D and 3D . After initially observing closed curves, which can be represented in a parametric form, we extended the method to connected compound curves—i.e. to connected configurations of a number of curves representable in a parametric form. In all cases, the measured linearities range over the interval (0,1], and do not change under translation, rotation and scaling transformations of the considered curve. We prove that the linearity is equal to 1 if and only if the measured curve consists of two straight line overlapping segments. The new linearity measure is theoretically well founded and all related statements are supported with rigorous mathematical proofs. The behavior and applicability of the new linearity measure are explained and illustrated by a number of experiments

Measuring linearity of curves in 2D and 3D

In this paper we define a new linearity measure for open curve segments in 2D and 3D . The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0,1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application. Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure

Combining behavioural types with security analysis

Today's software systems are highly distributed and interconnected, and they increasingly rely on communication to achieve their goals; due to their societal importance, security and trustworthiness are crucial aspects for the correctness of these systems. Behavioural types, which extend data types by describing also the structured behaviour of programs, are a widely studied approach to the enforcement of correctness properties in communicating systems. This paper offers a unified overview of proposals based on behavioural types which are aimed at the analysis of security properties