2,704 research outputs found
Verification for Timed Automata extended with Unbounded Discrete Data Structures
We study decidability of verification problems for timed automata extended
with unbounded discrete data structures. More detailed, we extend timed
automata with a pushdown stack. In this way, we obtain a strong model that may
for instance be used to model real-time programs with procedure calls. It is
long known that the reachability problem for this model is decidable. The goal
of this paper is to identify subclasses of timed pushdown automata for which
the language inclusion problem and related problems are decidable
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
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
Parametric timed automata extend timed automata (Alur and Dill, 1991) in that
they allow the specification of parametric bounds on the clock values. Since
their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the
emptiness problem for parametric timed automata with one clock is decidable,
whereas it is undecidable if the automaton uses three or more parametric
clocks. The problem is open for parametric timed automata with two parametric
clocks. Metric temporal logic, MTL for short, is a widely used specification
language for real-time systems. MTL-model checking of timed automata is
decidable, no matter how many clocks are used in the timed automaton. In this
paper, we prove that MTL-model checking for parametric timed automata is
undecidable, even if the automaton uses only one clock and one parameter and is
deterministic.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Revisiting Reachability in Timed Automata
We revisit a fundamental result in real-time verification, namely that the
binary reachability relation between configurations of a given timed automaton
is definable in linear arithmetic over the integers and reals. In this paper we
give a new and simpler proof of this result, building on the well-known
reachability analysis of timed automata involving difference bound matrices.
Using this new proof, we give an exponential-space procedure for model checking
the reachability fragment of the logic parametric TCTL. Finally we show that
the latter problem is NEXPTIME-hard
Path Checking for MTL and TPTL over Data Words
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are
quantitative extensions of linear temporal logic, which are prominent and
widely used in the verification of real-timed systems. It was recently shown
that the path checking problem for MTL, when evaluated over finite timed words,
is in the parallel complexity class NC. In this paper, we derive precise
complexity results for the path-checking problem for MTL and TPTL when
evaluated over infinite data words over the non-negative integers. Such words
may be seen as the behaviours of one-counter machines. For this setting, we
give a complete analysis of the complexity of the path-checking problem
depending on the number of register variables and the encoding of constraint
numbers (unary or binary). As the two main results, we prove that the
path-checking problem for MTL is P-complete, whereas the path-checking problem
for TPTL is PSPACE-complete. The results yield the precise complexity of model
checking deterministic one-counter machines against formulae of MTL and TPTL
The earlier the better: a theory of timed actor interfaces
Programming embedded and cyber-physical systems requires attention not only to functional behavior and correctness, but also to non-functional aspects and specifically timing and performance constraints. A structured, compositional, model-based approach based on stepwise refinement and abstraction techniques can support the development process, increase its quality and reduce development time through automation of synthesis, analysis or verification. For this purpose, we introduce in this paper a general theory of timed actor interfaces. Our theory supports a notion of refinement that is based on the principle of worst-case design that permeates the world of performance-critical systems. This is in contrast with the classical behavioral and functional refinements based on restricting or enlarging sets of behaviors. An important feature of our refinement is that it allows time-deterministic abstractions to be made of time-non-deterministic systems, improving efficiency and reducing complexity of formal analysis. We also show how our theory relates to, and can be used to reconcile a number of existing time and performance models and how their established theories can be exploited to represent and analyze interface specifications and refinement steps.\u
Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets
We analyze a timed Petri net model of an emergency call center which
processes calls with different levels of priority. The counter variables of the
Petri net represent the cumulated number of events as a function of time. We
show that these variables are determined by a piecewise linear dynamical
system. We also prove that computing the stationary regimes of the associated
fluid dynamics reduces to solving a polynomial system over a tropical
(min-plus) semifield of germs. This leads to explicit formul{\ae} expressing
the throughput of the fluid system as a piecewise linear function of the
resources, revealing the existence of different congestion phases. Numerical
experiments show that the analysis of the fluid dynamics yields a good
approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the
proceedings of the conference FORMATS 201
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