161 research outputs found
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Model Checking Synchronized Products of Infinite Transition Systems
Formal verification using the model checking paradigm has to deal with two
aspects: The system models are structured, often as products of components, and
the specification logic has to be expressive enough to allow the formalization
of reachability properties. The present paper is a study on what can be
achieved for infinite transition systems under these premises. As models we
consider products of infinite transition systems with different synchronization
constraints. We introduce finitely synchronized transition systems, i.e.
product systems which contain only finitely many (parameterized) synchronized
transitions, and show that the decidability of FO(R), first-order logic
extended by reachability predicates, of the product system can be reduced to
the decidability of FO(R) of the components. This result is optimal in the
following sense: (1) If we allow semifinite synchronization, i.e. just in one
component infinitely many transitions are synchronized, the FO(R)-theory of the
product system is in general undecidable. (2) We cannot extend the expressive
power of the logic under consideration. Already a weak extension of first-order
logic with transitive closure, where we restrict the transitive closure
operators to arity one and nesting depth two, is undecidable for an
asynchronous (and hence finitely synchronized) product, namely for the infinite
grid.Comment: 18 page
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