Permissive strategies in timed automata and games

Timed automata are a convenient framework for modelling and reasoning about real-time systems. While these models are now well-understood, they do not offer a convenient way of taking timing imprecisions into account. Several solutions (e.g. parametric guard enlargement) have been proposed over the last ten years to take such imprecisions into account. In this paper, we propose a novel approach for handling robust reachability, based on permissive strategies. While classical strategies propose to play an action at an exact point in time, permissive strategies consider intervals of possible dates when to play the selected action. In other words, the controller specifies an interval of time delays for actions to be executed in a more flexible way. With such a permissive strategy, we associate a penalty, which is the inverse of the length of the proposed interval, and accumulates along the run. We show that in that setting, optimal strategies can be computed in polynomial time for one-clock timed automata

Timed Parity Games: Complexity and Robustness

We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state} (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, \emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers

Automata-theoretic decision of timed games

The solution of games is a key decision problem in the context of verification of open systems and program synthesis. Given a game graph and a specification, we wish to determine if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification. In this paper, we consider timed games, where the game graph is a timed automaton and the specification is given by formulas of the temporal logics Ltl and Ctl. We present an automata-theoretic approach to solve the addressed games, extending to the timed framework a successful approach to solve discrete games. The main idea of this approach is to translate the timed automaton A, modeling the game graph, into a tree automaton AT accepting all trees that correspond to a strategy of the protagonist. Then, given an automaton corresponding to the specification, we intersect it with the tree automaton AT and check for the nonemptiness of the resulting automaton. Our approach yields a decision algorithm running in exponential time for Ctl and in double exponential time for Ltl. The obtained algorithms are optimal in the sense that their computational complexity matches the known lower bounds

Automata-theoretic Decision of Timed Games

The solution of games is a key decision problem in the context of veri cation of open systems and program synthesis. We present an automata-theoretic approach to solve timed games. Our solution gives a general framework to solve many classes of timed games via a translation to tree automata, extending to timed games a successful approach to solve discrete games. Our approach relies on translating a timed automaton into a tree automaton that accepts all the trees corresponding to a given strategy of the protagonist. This construction exploits the region automaton introduced by Alur and Dill. We use our framework to solve timed B\u7fuchi games in exponential time, timed Rabin games in exponential time, Ctl games in exponential time and Ltl games in doubly exponential time. All these results are tight in the sense that they match the known lower bounds on these decision problems