609 research outputs found
Fast algorithms for handling diagonal constraints in timed automata
A popular method for solving reachability in timed automata proceeds by
enumerating reachable sets of valuations represented as zones. A na\"ive
enumeration of zones does not terminate. Various termination mechanisms have
been studied over the years. Coming up with efficient termination mechanisms
has been remarkably more challenging when the automaton has diagonal
constraints in guards.
In this paper, we propose a new termination mechanism for timed automata with
diagonal constraints based on a new simulation relation between zones.
Experiments with an implementation of this simulation show significant gains
over existing methods.Comment: Shorter version of this article to appear in CAV 201
A Unified Model for Real-Time Systems: Symbolic Techniques and Implementation
In this paper, we consider a model of generalized timed automata (GTA) with
two kinds of clocks, history and future, that can express many timed features
succinctly, including timed automata, event-clock automata with and without
diagonal constraints, and automata with timers.
Our main contribution is a new simulation-based zone algorithm for checking
reachability in this unified model. While such algorithms are known to exist
for timed automata, and have recently been shown for event-clock automata
without diagonal constraints, this is the first result that can handle
event-clock automata with diagonal constraints and automata with timers. We
also provide a prototype implementation for our model and show experimental
results on several benchmarks. To the best of our knowledge, this is the first
effective implementation not just for our unified model, but even just for
automata with timers or for event-clock automata (with predicting clocks)
without going through a costly translation via timed automata. Last but not
least, beyond being interesting in their own right, generalized timed automata
can be used for model-checking event-clock specifications over timed automata
models
Reachability in Timed Automata with Diagonal Constraints
We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test Z <= Z\u27 which ascertains that zone Z does not reach more states than zone Z\u27, and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. We propose a simulation relation <=_{LU}^d for timed automata with diagonal constraints. On the negative side, we show that deciding Z not <=_{LU}^d Z\u27 is NP-complete. On the positive side, we identify a witness for Z not <=_{LU}^d Z\u27 and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice
Zone-based verification of timed automata: extrapolations, simulations and what next?
Timed automata have been introduced by Rajeev Alur and David Dill in the
early 90's. In the last decades, timed automata have become the de facto model
for the verification of real-time systems. Algorithms for timed automata are
based on the traversal of their state-space using zones as a symbolic
representation. Since the state-space is infinite, termination relies on finite
abstractions that yield a finite representation of the reachable states.
The first solution to get finite abstractions was based on extrapolations of
zones, and has been implemented in the industry-strength tool Uppaal. A
different approach based on simulations between zones has emerged in the last
ten years, and has been implemented in the fully open source tool TChecker. The
simulation-based approach has led to new efficient algorithms for reachability
and liveness in timed automata, and has also been extended to richer models
like weighted timed automata, and timed automata with diagonal constraints and
updates.
In this article, we survey the extrapolation and simulation techniques, and
discuss some open challenges for the future.Comment: Invited contribution at FORMATS'2
Timed pushdown automata revisited
This paper contains two results on timed extensions of pushdown automata
(PDA). As our first result we prove that the model of dense-timed PDA of
Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with
timeless stack. Motivated by this result, we advocate the framework of
first-order definable PDA, a specialization of PDA in sets with atoms, as the
right setting to define and investigate timed extensions of PDA. The general
model obtained in this way is Turing complete. As our second result we prove
NEXPTIME upper complexity bound for the non-emptiness problem for an expressive
subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more
restrictive subclass of PDA with timeless stack, thus subsuming the complexity
bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape
Quantitative model checking of continuous-time Markov chains against timed automata specifications
We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud
accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations
Better abstractions for timed automata
We consider the reachability problem for timed automata. A standard solution
to this problem involves computing a search tree whose nodes are abstractions
of zones. These abstractions preserve underlying simulation relations on the
state space of the automaton. For both effectiveness and efficiency reasons,
they are parametrized by the maximal lower and upper bounds (LU-bounds)
occurring in the guards of the automaton. We consider the aLU abstraction
defined by Behrmann et al. Since this abstraction can potentially yield
non-convex sets, it has not been used in implementations. We prove that aLU
abstraction is the biggest abstraction with respect to LU-bounds that is sound
and complete for reachability. We also provide an efficient technique to use
the aLU abstraction to solve the reachability problem.Comment: Extended version of LICS 2012 paper (conference paper till v6). in
Information and Computation, available online 27 July 201
Polynomial Interrupt Timed Automata
Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where
reachability and some variants of timed model checking are decidable even in
presence of parameters. They are well suited to model and analyze real-time
operating systems. Here we extend ITA with polynomial guards and updates,
leading to the class of polynomial ITA (PolITA). We prove the decidability of
the reachability and model checking of a timed version of CTL by an adaptation
of the cylindrical decomposition method for the first-order theory of reals.
Compared to previous approaches, our procedure handles parameters and clocks in
a unified way. Moreover, we show that PolITA are incomparable with stopwatch
automata. Finally additional features are introduced while preserving
decidability
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