909 research outputs found
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
Model checking synchronized products of infinite transition systems
Abstract. 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 firstorder 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. 1
The First-Order Theory of Ground Tree Rewrite Graphs
We prove that the complexity of the uniform first-order theory of ground tree
rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower
bound, we show that there is some fixed ground tree rewrite graph whose
first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to
logspace reductions. Finally, we prove that there exists a fixed ground tree
rewrite graph together with a single unary predicate in form of a regular tree
language such that the resulting structure has a non-elementary first-order
theory.Comment: accepted for Logical Methods in Computer Scienc
On Descriptive Complexity, Language Complexity, and GB
We introduce , a monadic second-order language for reasoning about
trees which characterizes the strongly Context-Free Languages in the sense that
a set of finite trees is definable in iff it is (modulo a
projection) a Local Set---the set of derivation trees generated by a CFG. This
provides a flexible approach to establishing language-theoretic complexity
results for formalisms that are based on systems of well-formedness constraints
on trees. We demonstrate this technique by sketching two such results for
Government and Binding Theory. First, we show that {\em free-indexation\/}, the
mechanism assumed to mediate a variety of agreement and binding relationships
in GB, is not definable in and therefore not enforcible by CFGs.
Second, we show how, in spite of this limitation, a reasonably complete GB
account of English can be defined in . Consequently, the language
licensed by that account is strongly context-free. We illustrate some of the
issues involved in establishing this result by looking at the definition, in
, of chains. The limitations of this definition provide some insight
into the types of natural linguistic principles that correspond to higher
levels of language complexity. We close with some speculation on the possible
significance of these results for generative linguistics.Comment: To appear in Specifying Syntactic Structures, papers from the Logic,
Structures, and Syntax workshop, Amsterdam, Sept. 1994. LaTeX source with
nine included postscript figure
A Logic of Reachable Patterns in Linked Data-Structures
We define a new decidable logic for expressing and checking invariants of
programs that manipulate dynamically-allocated objects via pointers and
destructive pointer updates. The main feature of this logic is the ability to
limit the neighborhood of a node that is reachable via a regular expression
from a designated node. The logic is closed under boolean operations
(entailment, negation) and has a finite model property. The key technical
result is the proof of decidability. We show how to express precondition,
postconditions, and loop invariants for some interesting programs. It is also
possible to express properties such as disjointness of data-structures, and
low-level heap mutations. Moreover, our logic can express properties of
arbitrary data-structures and of an arbitrary number of pointer fields. The
latter provides a way to naturally specify postconditions that relate the
fields on entry to a procedure to the fields on exit. Therefore, it is possible
to use the logic to automatically prove partial correctness of programs
performing low-level heap mutations
Computational Processes and Incompleteness
We introduce a formal definition of Wolfram's notion of computational process
based on cellular automata, a physics-like model of computation. There is a
natural classification of these processes into decidable, intermediate and
complete. It is shown that in the context of standard finite injury priority
arguments one cannot establish the existence of an intermediate computational
process
Parameterized Model-Checking for Timed-Systems with Conjunctive Guards (Extended Version)
In this work we extend the Emerson and Kahlon's cutoff theorems for process
skeletons with conjunctive guards to Parameterized Networks of Timed Automata,
i.e. systems obtained by an \emph{apriori} unknown number of Timed Automata
instantiated from a finite set of Timed Automata templates.
In this way we aim at giving a tool to universally verify software systems
where an unknown number of software components (i.e. processes) interact with
continuous time temporal constraints. It is often the case, indeed, that
distributed algorithms show an heterogeneous nature, combining dynamic aspects
with real-time aspects. In the paper we will also show how to model check a
protocol that uses special variables storing identifiers of the participating
processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is
non-trivial, since solutions to the parameterized verification problem often
relies on the processes to be symmetric, i.e. indistinguishable. On the other
side, many popular distributed algorithms make use of PIDs and thus cannot
directly apply those solutions
Collapsible Pushdown Graphs of Level 2 are Tree-Automatic
We show that graphs generated by collapsible pushdown systems of level 2 are
tree-automatic. Even when we allow -contractions and add a
reachability predicate (with regular constraints) for pairs of configurations,
the structures remain tree-automatic. Hence, their FO theories are decidable,
even when expanded by a reachability predicate. As a corollary, we obtain the
tree-automaticity of the second level of the Caucal-hierarchy.Comment: 12 pages Accepted for STACS 201
An Optimal Decision Procedure for MPNL over the Integers
Interval temporal logics provide a natural framework for qualitative and
quantitative temporal reason- ing over interval structures, where the truth of
formulae is defined over intervals rather than points. In this paper, we study
the complexity of the satisfiability problem for Metric Propositional Neigh-
borhood Logic (MPNL). MPNL features two modalities to access intervals "to the
left" and "to the right" of the current one, respectively, plus an infinite set
of length constraints. MPNL, interpreted over the naturals, has been recently
shown to be decidable by a doubly exponential procedure. We improve such a
result by proving that MPNL is actually EXPSPACE-complete (even when length
constraints are encoded in binary), when interpreted over finite structures,
the naturals, and the in- tegers, by developing an EXPSPACE decision procedure
for MPNL over the integers, which can be easily tailored to finite linear
orders and the naturals (EXPSPACE-hardness was already known).Comment: In Proceedings GandALF 2011, arXiv:1106.081
- …