Constraint-based reachability
نویسندگان
چکیده
Interpretation (AI) is a theoretical framework introduced by Cousot and Cousot in [10] to manipulate abstractions of program states. An abstraction can be used to simplify program analysis problems otherwise not computable in realistic time, to manageable problems more easily solvable. Instead of working on the concrete semantics of a program1, AI computes results over an abstract semantics allowing so to produce over-approximating properties of the concrete semantics. In the following we introduce the basic notions required to understand AI. Definition 1 (Partially ordered set (poset)) Let ⊑ be a partial order law, then the pair (D ,⊑) is called a poset iff ∀x ∈ D ,x ⊑ x (reflexive) ∀x,y ∈ D ,x ⊑ y∧ y ⊑ x =⇒ x = y (anti-symmetry) ∀x,y,z ∈ D ,x ⊑ y∧ y ⊑ z =⇒ x ⊑ z (transitive) 1Program semantics captures formally all the possible behaviours of a program. A. Gotlieb, T. Denmat, N. Lazaar 27 Definition 2 (Complete lattice) A complete lattice is a 4-tuple (D ,⊑, ⊔ , d ) such that
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