Systematic design of complete abstractions: from
semantics to program analysis via model-checking
By: Roberto Giacobazzi
Roberto
Giacobazzi
Dip. di Informatica
Univ. di Verona
Strada Le Grazie a Ca' Vignal 2
I-37134 Verona, Italy
giaco@sci.univr.it
Abstract:
Completeness is a desirable feature of any abstraction,
formalizing the intuition that, relatively to the approximated
observables, there is no loss of information which is accumulated by
approximating computations in the corresponding abstract domain. In
this talk we consider the problem of making abstract interpretations
complete by minimally refining or simplifying abstract domains. We
provide a constructive characterization for the least complete
refinement and the greatest complete simplification of abstractions
relatively to a forward/backward semantics. We show how this theory
can be used to derive both effective algorithms for manipulating and
comparing abstract interpretations and to better understand the power
and limitations of known abstractions in semantics, program analysis
and model-checking. We show that compositional semantics abstracting
maximal traces of a transition system can be systematically derived by
making the abstraction complete for trace concatenation. Then,
starting from Cousot's proof that state-based model-checking is
incomplete with respect to the trace-based semantics of an enhanced
mu-calculus, we show that there is no way to make it complete unless
having traces them self in the model or by considering straightforward
abstractions asserting that a trace is a trace. This proves that any
state-based model checking is intrinsically incomplete with respect to
the trace-based semantics of the mu-calculus. We conclude by giving a
constructive characterization of Clarke et al.'s spurious
counterexamples in terms of completeness of the underlying abstract
interpretation. This result allows us to understand the structure of
the counterexamples produced by a model-checker that can be removed by
systematically refining abstractions.
The results presented in the talk have been obtained jointly with:
Isabella Mastroeni, Elisa Quintarelli, Francesco Ranzato, and
Francesca Scozzari.
Related papers:
giaco@sci.univr.it