salle A. Turing CE4
9 mai 2012 - 14h00
A Perfect Model for Bounded Verification
par Pierre Ganty de IMDEA (Madrid)
Résumé : A class of languages C is perfect if it is closed under
Boolean operations and the emptiness problem is decidable. Perfect
language classes are the basis for the automata-theoretic approach to
model checking: a system is correct if the language generated by the
system is disjoint from the language of bad traces. Regular languages
are perfect, but because the disjointness problem for CFLs is
undecidable, no class containing the CFLs can be perfect.
In practice, verification problems for language classes that are
not perfect are often under-approximated by checking if the property
holds for all behaviors of the system belonging to a fixed subset. A
general way to specify a subset of behaviors is by using bounded
languages (languages of the form w1* ... wk* for fixed words
w1,...,wk). A class of languages C is perfect modulo bounded languages
if it is closed under Boolean operations relative to every bounded
language, and if the emptiness problem is decidable relative to every
bounded language.
We consider finding perfect classes of languages modulo bounded
languages. We show that the class of languages accepted by multi-head
pushdown automata are perfect modulo bounded languages, and
characterize the complexities of decision problems. We show that
computations of several known models of systems, such as recursive
multi-threaded programs, recursive counter machines, and communicating
finite-state machines can be encoded as multi-head pushdown automata,
giving uniform and optimal underapproximation algorithms modulo
bounded languages.
[Joint work with Javier Esparza and Rupak Majumdar]
