Object-oriented inheritance of statecharts for control applications

This paper discusses how object-oriented iuheritance can be re-interpreted if statecharts are used for modelling the dynamic behaviour of an object. The support of inheritance of statecharts allows the improvement of systems' development by easing the reutilization of parts of already developed euccessful systems, aad by promoting the iterative and continuous models' refinement advocated by the operatioaal approach. Statechart is the formalism used within UML to specify reactive state.based behaviours. This paper covers the use of statecharts within the modelling of embedded systems for industrial control applxications, where performance and memory usage are main concerns.

Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.