Abstract This article presents the systematic design of a class of relational numerical abstract domains from non-relational ones. Constructed domains represent sets of invariants of the form (vj − vi ∈ C), where vj and vi are two variables, and C lives in an abstraction of P(Z), P(Q), or P(R). We will call this family of domains weakly relational domains. The underlying concept allowing this construction is an extension of potential graphs and shortest-path closure algorithms in exotic-like algebras. Example constructions are given in order to retrieve well-known domains Interpretation framework in order to design various static analyses. A major benefit of this construction is its modularity, allowing to quickly implement new abstract domains from existing ones. 1

Binary Decision Graphs are an extension of Binary Decision Diagrams that can represent some infinite boolean functions. Three refinements of BDGs corresponding to classes of infinite functions of increasing complexity are presented. The first one is closed by intersection and union, the second one by intersection, and the last one by all boolean operations. The first two classes give rise to a canonical representation, which, when restricted to finite functions, are the classical BDDs. The paper also gives new insights in to the notion of variable names and the possibility of sharing variable names that can be of interest in the case of finite functions.

Ecient storage of types within a compiler is necessary to avoid large blowups in space during compilation.

Communication protocols can be formally described by the Communicating Finite-State Machines (CFSM) model. This model is expressive, but not expressive enough to deal with complex protocols that involve structured messages encapsulating integers or lists of integers. This is the reason why we propose an extension of this model: the Symbolic Communicating Machines (SCM). We also propose an approximate reachability analysis method, based on lattice automata. Lattice automata are finite automata, the transitions of which are labeled with elements of an atomic lattice. We tackle the problem of the determinization as well as the definition of a widening operator for these automata. We also show that lattice automata are useful for the interprocedural analysis.

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