An Algebraic Approach to the Static Analysis of Concurrent Software
نویسنده
چکیده
interpretation of path languages Let L = (2Act,⊆,∪,∩, ∅,Act∗) be the complete lattice of languages over Act An abstraction consists of an abstract lattice D = (D,v,t,u,⊥,>), and a Galois connection L α γ D γ(α(L)) ⊇ L (A ⊇ L) γ(d1 u d2) = γ(d1) ∩ γ(d2) (u matches ∩) α(L) is the abstract object representing the language A ⊇ L γ(α(L)) is the language A 16 An abstraction α1(L) is the pair [F ,R], F ,R ⊆ Act , where F (for forbidden) is the set of actions that do not occur in any word of L R (for required) is the set of actions that occur in all words of L Example: for Act = {a, b, c}, α1(ab∗) = [{c}, {a}] γ1([F ,R]) = all words containing no letter of F and all letters of R [F1,R1] u [F2,R2] = [F1 ∪ F2,R1 ∪ R2] (well, almost true . . . )
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