1,066 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
O-Minimal Hybrid Reachability Games
In this paper, we consider reachability games over general hybrid systems,
and distinguish between two possible observation frameworks for those games:
either the precise dynamics of the system is seen by the players (this is the
perfect observation framework), or only the starting point and the delays are
known by the players (this is the partial observation framework). In the first
more classical framework, we show that time-abstract bisimulation is not
adequate for solving this problem, although it is sufficient in the case of
timed automata . That is why we consider an other equivalence, namely the
suffix equivalence based on the encoding of trajectories through words. We show
that this suffix equivalence is in general a correct abstraction for games. We
apply this result to o-minimal hybrid systems, and get decidability and
computability results in this framework. For the second framework which assumes
a partial observation of the dynamics of the system, we propose another
abstraction, called the superword encoding, which is suitable to solve the
games under that assumption. In that framework, we also provide decidability
and computability results
Optimal Reachability in Divergent Weighted Timed Games
Weighted timed games are played by two players on a timed automaton equipped
with weights: one player wants to minimise the accumulated weight while
reaching a target, while the other has an opposite objective. Used in a
reactive synthesis perspective, this quantitative extension of timed games
allows one to measure the quality of controllers. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. Decidability results exist for subclasses of one-clock
games, and for a subclass with non-negative weights defined by a semantical
restriction on the weights of cycles. In this work, we introduce the class of
divergent weighted timed games as a generalisation of this semantical
restriction to arbitrary weights. We show how to compute their optimal value,
yielding the first decidable class of weighted timed games with negative
weights and an arbitrary number of clocks. In addition, we prove that
divergence can be decided in polynomial space. Last, we prove that for untimed
games, this restriction yields a class of games for which the value can be
computed in polynomial time
Revisiting Robustness in Priced Timed Games
Priced timed games are optimal-cost reachability games played between two
players---the controller and the environment---by moving a token along the
edges of infinite graphs of configurations of priced timed automata. The goal
of the controller is to reach a given set of target locations as cheaply as
possible, while the goal of the environment is the opposite. Priced timed games
are known to be undecidable for timed automata with or more clocks, while
they are known to be decidable for automata with clock.
In an attempt to recover decidability for priced timed games Bouyer, Markey,
and Sankur studied robust priced timed games where the environment has the
power to slightly perturb delays proposed by the controller. Unfortunately,
however, they showed that the natural problem of deciding the existence of
optimal limit-strategy---optimal strategy of the controller where the
perturbations tend to vanish in the limit---is undecidable with or more
clocks. In this paper we revisit this problem and improve our understanding of
the decidability of these games. We show that the limit-strategy problem is
already undecidable for a subclass of robust priced timed games with or
more clocks. On a positive side, we show the decidability of the existence of
almost optimal strategies for the same subclass of one-clock robust priced
timed games by adapting a classical construction by Bouyer at al. for one-clock
priced timed games
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata
Markov automata combine continuous time, probabilistic transitions, and
nondeterminism in a single model. They represent an important and powerful way
to model a wide range of complex real-life systems. However, such models tend
to be large and difficult to handle, making abstraction and abstraction
refinement necessary. In this paper we present an abstraction and abstraction
refinement technique for Markov automata, based on the game-based and
menu-based abstraction of probabilistic automata. First experiments show that a
significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Probabilistic Timed Automata with Clock-Dependent Probabilities
Probabilistic timed automata are classical timed automata extended with
discrete probability distributions over edges. We introduce clock-dependent
probabilistic timed automata, a variant of probabilistic timed automata in
which transition probabilities can depend linearly on clock values.
Clock-dependent probabilistic timed automata allow the modelling of a
continuous relationship between time passage and the likelihood of system
events. We show that the problem of deciding whether the maximum probability of
reaching a certain location is above a threshold is undecidable for
clock-dependent probabilistic timed automata. On the other hand, we show that
the maximum and minimum probability of reaching a certain location in
clock-dependent probabilistic timed automata can be approximated using a
region-graph-based approach.Comment: Full version of a paper published at RP 201
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