111 research outputs found
Two-Player Reachability-Price Games on Single-Clock Timed Automata
We study two player reachability-price games on single-clock timed automata.
The problem is as follows: given a state of the automaton, determine whether
the first player can guarantee reaching one of the designated goal locations.
If a goal location can be reached then we also want to compute the optimum
price of doing so. Our contribution is twofold. First, we develop a theory of
cost functions, which provide a comprehensive methodology for the analysis of
this problem. This theory allows us to establish our second contribution, an
EXPTIME algorithm for computing the optimum reachability price, which improves
the existing 3EXPTIME upper bound.Comment: In Proceedings QAPL 2011, arXiv:1107.074
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
Optimal Control for Multi-mode Systems with Discrete Costs
This paper studies optimal time-bounded control in multi-mode systems with
discrete costs. Multi-mode systems are an important subclass of linear hybrid
systems, in which there are no guards on transitions and all invariants are
global. Each state has a continuous cost attached to it, which is linear in the
sojourn time, while a discrete cost is attached to each transition taken. We
show that an optimal control for this model can be computed in NEXPTIME and
approximated in PSPACE. We also show that the one-dimensional case is simpler:
although the problem is NP-complete (and in LOGSPACE for an infinite time
horizon), we develop an FPTAS for finding an approximate solution.Comment: extended version of a FORMATS 2017 pape
Mean-Payoff Games on Timed Automata
Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players - Player Min and Player Max - by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space
A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems
Physical systems can fail. For this reason the problem of identifying and
reacting to faults has received a large attention in the control and computer
science communities. In this paper we study the fault diagnosis problem for
hybrid systems from a game-theoretical point of view. A hybrid system is a
system mixing continuous and discrete behaviours that cannot be faithfully
modeled neither by using a formalism with continuous dynamics only nor by a
formalism including only discrete dynamics. We use the well known framework of
hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis
Game on them, using two players: the environment and the diagnoser. The
environment controls the evolution of the system and chooses whether and when a
fault occurs. The diagnoser observes the external behaviour of the system and
announces whether a fault has occurred or not. Existence of a winning strategy
for the diagnoser implies that faults can be detected correctly, while
computing such a winning strategy corresponds to implement a diagnoser for the
system. We will show how to determine the existence of a winning strategy, and
how to compute it, for some decidable classes of hybrid automata like o-minimal
hybrid automata.Comment: In Proceedings GandALF 2011, arXiv:1106.081
- …