215 research outputs found
Minimum-Cost Reachability for Priced Timed Automata
This paper introduces the model of linearly priced timed automata as an extension of timed automata, with prices on both transitions and locations. For this model we consider the minimum-cost reachability problem: i.e. given a linearly priced timed automaton and a targetstate, determine the minimum cost of executions from the initial state to the target state. This problem generalizes the minimum-time reachability problem for ordinary timed automata. We prove decidability of this problem by offering an algorithmic solution, which is based on a combination of branch-and-bound techniques and a new notion of priced regions. The latter allows symbolic representation and manipulation of reachable states together with the cost of reaching them.Keywords: Timed Automata, Verification, Data Structures, Algorithms,Optimization
Optimal infinite scheduling for multi-priced timed automata
This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules
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
Model Checking One-clock Priced Timed Automata
We consider the model of priced (a.k.a. weighted) timed automata, an
extension of timed automata with cost information on both locations and
transitions, and we study various model-checking problems for that model based
on extensions of classical temporal logics with cost constraints on modalities.
We prove that, under the assumption that the model has only one clock,
model-checking this class of models against the logic WCTL, CTL with
cost-constrained modalities, is PSPACE-complete (while it has been shown
undecidable as soon as the model has three clocks). We also prove that
model-checking WMTL, LTL with cost-constrained modalities, is decidable only if
there is a single clock in the model and a single stopwatch cost variable
(i.e., whose slopes lie in {0,1}).Comment: 28 page
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
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
Simple Priced Timed Games Are Not That Simple
Priced timed games are two-player zero-sum games played on priced timed
automata (whose locations and transitions are labeled by weights modeling the
costs of spending time in a state and executing an action, respectively). The
goals of the players are to minimise and maximise the cost to reach a target
location, respectively. We consider priced timed games with one clock and
arbitrary (positive and negative) weights and show that, for an important
subclass of theirs (the so-called simple priced timed games), one can compute,
in exponential time, the optimal values that the players can achieve, with
their associated optimal strategies. As side results, we also show that
one-clock priced timed games are determined and that we can use our result on
simple priced timed games to solve the more general class of so-called
reset-acyclic priced timed games (with arbitrary weights and one-clock)
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