17,575 research outputs found
Model-Checking the Higher-Dimensional Modal mu-Calculus
The higher-dimensional modal mu-calculus is an extension of the mu-calculus
in which formulas are interpreted in tuples of states of a labeled transition
system. Every property that can be expressed in this logic can be checked in
polynomial time, and conversely every polynomial-time decidable problem that
has a bisimulation-invariant encoding into labeled transition systems can also
be defined in the higher-dimensional modal mu-calculus. We exemplify the latter
connection by giving several examples of decision problems which reduce to
model checking of the higher-dimensional modal mu-calculus for some fixed
formulas. This way generic model checking algorithms for the logic can then be
used via partial evaluation in order to obtain algorithms for theses problems
which may benefit from improvements that are well-established in the field of
program verification, namely on-the-fly and symbolic techniques. The aim of
this work is to extend such techniques to other fields as well, here
exemplarily done for process equivalences, automata theory, parsing, string
problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317
Relational semantics of linear logic and higher-order model-checking
In this article, we develop a new and somewhat unexpected connection between
higher-order model-checking and linear logic. Our starting point is the
observation that once embedded in the relational semantics of linear logic, the
Church encoding of any higher-order recursion scheme (HORS) comes together with
a dual Church encoding of an alternating tree automata (ATA) of the same
signature. Moreover, the interaction between the relational interpretations of
the HORS and of the ATA identifies the set of accepting states of the tree
automaton against the infinite tree generated by the recursion scheme. We show
how to extend this result to alternating parity automata (APT) by introducing a
parametric version of the exponential modality of linear logic, capturing the
formal properties of colors (or priorities) in higher-order model-checking. We
show in particular how to reunderstand in this way the type-theoretic approach
to higher-order model-checking developed by Kobayashi and Ong. We briefly
explain in the end of the paper how his analysis driven by linear logic results
in a new and purely semantic proof of decidability of the formulas of the
monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
Using models to model-check recursive schemes
We propose a model-based approach to the model checking problem for recursive
schemes. Since simply typed lambda calculus with the fixpoint operator,
lambda-Y-calculus, is equivalent to schemes, we propose the use of a model of
lambda-Y-calculus to discriminate the terms that satisfy a given property. If a
model is finite in every type, this gives a decision procedure. We provide a
construction of such a model for every property expressed by automata with
trivial acceptance conditions and divergence testing. Such properties pose
already interesting challenges for model construction. Moreover, we argue that
having models capturing some class of properties has several other virtues in
addition to providing decidability of the model-checking problem. As an
illustration, we show a very simple construction transforming a scheme to a
scheme reflecting a property captured by a given model.Comment: Long version of a paper presented at TLCA 201
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of
hybrid automata well suited to the description of timed multi-task systems with
interruptions in a single processor environment. While the reachability problem
is undecidable for hybrid automata we show that it is decidable for ITA. More
precisely we prove that the untimed language of an ITA is regular, by building
a finite automaton as a generalized class graph. We then establish that the
reachability problem for ITA is in NEXPTIME and in PTIME when the number of
clocks is fixed. To prove the first result, we define a subclass ITA- of ITA,
and show that (1) any ITA can be reduced to a language-equivalent automaton in
ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without
any class graph). In the next step, we investigate the verification of real
time properties over ITA. We prove that model checking SCL, a fragment of a
timed linear time logic, is undecidable. On the other hand, we give model
checking procedures for two fragments of timed branching time logic. We also
compare the expressive power of classical timed automata and ITA and prove that
the corresponding families of accepted languages are incomparable. The result
also holds for languages accepted by controlled real-time automata (CRTA), that
extend timed automata. We finally combine ITA with CRTA, in a model which
encompasses both classes and show that the reachability problem is still
decidable. Additionally we show that the languages of ITA are neither closed
under complementation nor under intersection
- âŠ