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Abstract Interpretations in the Framework of Invariant Sets

Alexandru A., Ciobanu G.

Fundamenta Informaticae

2016

Vol. 144, nr 1

1--22

We present a theory of abstract interpretations in the framework of invariant sets by translating the notions of lattices and Galois connections into this framework, and presenting their properties in terms of finitely supported objects. We introduce the notions of invariant correctness relation and invariant representation function, emphasize an equivalence between them, and establish the relationship between these notions and invariant Galois connections. Finally, we provide some widening and narrowing techniques in order to approximate the least fixed points of finitely supported transition functions.

Nominal Groups and Their Homomorphism Theorems

Alexandru A., Ciobanu G.

Fundamenta Informaticae

2014

Vol. 131, nr 3-4

279--298

We introduce and study the nominal groups, providing some algebraic properties of this new structure. We focus on the properties of nominal homomorphisms, and study the correspondence between some results obtained in the Fraenkel-Mostowski framework (where only finitely supported objects are allowed) and those obtained in the classical Zermelo-Fraenkel framework.