10 research outputs found
Competitive optimisation on timed automata
Timed automata are finite automata accompanied by a finite set of real-valued variables called clocks. Optimisation problems on timed automata are fundamental to the verification of properties of real-time systems modelled as timed automata, while the control-program synthesis problem of such systems can be modelled as a two-player game. This thesis presents a study of optimisation problems and two-player games on timed automata under a general heading of competitive optimisation on timed automata.
This thesis views competitive optimisation on timed automata as a multi-stage decision process, where one or two players are confronted with the problem of choosing a sequence of timed movesâa time delay and an actionâin order to optimise their objectives. A solution of such problems consists of the âoptimalâ value of the objective and an âoptimalâ strategy for each player. This thesis introduces a novel class of strategies, called boundary strategies, that suggest to a player a symbolic timed move of the form (b, c, a)â âwait until the value of the clock c is in very close proximity of the integer b, and then execute a transition labelled with the action aâ. A distinctive feature of the competitive optimisation problems discussed in this thesis is the existence of optimal boundary strategies. Surprisingly perhaps, many competitive optimisation problems on timed automata of practical interest admit optimal boundary strategies. For example, optimisation problems with reachability price, discounted price, and average-price objectives, and two-player turn-based games with reachability time and average time objectives.
The existence of optimal boundary strategies allows one to work with a novel abstraction of timed automata, called a boundary region graph, where players can use only boundary strategies. An interesting property of a boundary region graph is that, for every state, the set of reachable states is finite. Hence, the existence of optimal boundary strategies permits us to reduce competitive optimisation problem on a timed automaton to the corresponding competitive optimisation problem on a finite graph
Competative optimisation on timed automata
Timed automata are finite automata accompanied by a finite set of real-valued variables called clocks. Optimisation problems on timed automata are fundamental to the verification of properties of real-time systems modelled as timed automata, while the control-program synthesis problem of such systems can be modelled as a two-player game. This thesis presents a study of optimisation problems and two-player games on timed automata under a general heading of competitive optimisation on timed automata. This thesis views competitive optimisation on timed automata as a multi-stage decision process, where one or two players are confronted with the problem of choosing a sequence of timed movesâa time delay and an actionâin order to optimise their objectives. A solution of such problems consists of the âoptimalâ value of the objective and an âoptimalâ strategy for each player. This thesis introduces a novel class of strategies, called boundary strategies, that suggest to a player a symbolic timed move of the form (b, c, a)â âwait until the value of the clock c is in very close proximity of the integer b, and then execute a transition labelled with the action aâ. A distinctive feature of the competitive optimisation problems discussed in this thesis is the existence of optimal boundary strategies. Surprisingly perhaps, many competitive optimisation problems on timed automata of practical interest admit optimal boundary strategies. For example, optimisation problems with reachability price, discounted price, and average-price objectives, and two-player turn-based games with reachability time and average time objectives. The existence of optimal boundary strategies allows one to work with a novel abstraction of timed automata, called a boundary region graph, where players can use only boundary strategies. An interesting property of a boundary region graph is that, for every state, the set of reachable states is finite. Hence, the existence of optimal boundary strategies permits us to reduce competitive optimisation problem on a timed automaton to the corresponding competitive optimisation problem on a finite graph.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Solving Parity Games on Integer Vectors
We consider parity games on infinite graphs where configurations are
represented by control-states and integer vectors. This framework subsumes two
classic game problems: parity games on vector addition systems with states
(vass) and multidimensional energy parity games. We show that the
multidimensional energy parity game problem is inter-reducible with a subclass
of single-sided parity games on vass where just one player can modify the
integer counters and the opponent can only change control-states. Our main
result is that the minimal elements of the upward-closed winning set of these
single-sided parity games on vass are computable. This implies that the Pareto
frontier of the minimal initial credit needed to win multidimensional energy
parity games is also computable, solving an open question from the literature.
Moreover, our main result implies the decidability of weak simulation
preorder/equivalence between finite-state systems and vass, and the
decidability of model checking vass with a large fragment of the modal
mu-calculus.Comment: 30 page
Priced Timed Petri Nets
We consider priced timed Petri nets, i.e., unbounded Petri nets where each
token carries a real-valued clock. Transition arcs are labeled with time
intervals, which specify constraints on the ages of tokens. Furthermore, our
cost model assigns token storage costs per time unit to places, and firing
costs to transitions. This general model strictly subsumes both priced timed
automata and unbounded priced Petri nets. We study the cost of computations
that reach a given control-state. In general, a computation with minimal cost
may not exist, due to strict inequalities in the time constraints. However, we
show that the infimum of the costs to reach a given control-state is computable
in the case where all place and transition costs are non-negative. On the other
hand, if negative costs are allowed, then the question whether a given
control-state is reachable with zero overall cost becomes undecidable. In fact,
this negative result holds even in the simpler case of discrete time (i.e.,
integer-valued clocks).Comment: 51 pages. LMCS journal version of arXiv:1104.061
Concavely-Priced Timed Automata (Extended Abstract)
Concavely-priced timed automata, a generalization of linearly-priced timed automata, are introduced. Computing the minimum value of a number of cost functions-including reachability price, discounted price, average time, average price, price-per-time average, and price-per-reward average-is considered in a uniform fashion for concavely-priced timed automata. All the corresponding decision problems are shown to be PSPACE-complete. This paper generalises the recent work of Bouyer et al. on deciding the minimum reachability price and the minimum ratio-price for linearly-priced timed automata.
A new type of a region graph-the boundary region graph-is defined, which generalizes the corner-point abstraction of Bouyer et al. A broad class of cost functions-concave-regular cost functions-is introduced, and the boundary region graph is shown to be a correct abstraction for deciding the minimum value of concave-regular cost functions for concavely-priced timed automata