Automata-theoretic decision of timed games (original) (raw)

Reachability-time games on timed automata

2007

In a reachability-time game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachability-time games on strongly non-Zeno timed automata using a value iteration algorithm. This paper complements their work by providing a strategy improvement algorithm for the problem.

Improved Undecidability Results for Reachability Games on Recursive Timed Automata

Electronic Proceedings in Theoretical Computer Science, 2014

We study reachability games on recursive timed automata (RTA) that generalize Alur-Dill timed automata with recursive procedure invocation mechanism similar to recursive state machines. It is known that deciding the winner in reachability games on RTA is undecidable for automata with two or more clocks, while the problem is decidable for automata with only one clock. Ouaknine and Worrell recently proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. We revisited games on recursive timed automata with time-bounded restriction in the hope of recovering decidability. However, we found that the problem still remains undecidable for recursive timed automata with three or more clocks. Using similar proof techniques we characterize a decidability frontier for a generalization of RTA to recursive stopwatch automata.

Efficient On-the-Fly Algorithms for the Analysis of Timed Games

Lecture Notes in Computer Science, 2005

In this paper, we propose a first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties 1 . The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka [15] for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the algorithm are carried out efficiently by the use of so-called zones as the underlying data structure. Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining time-optimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.

From Timed Automata to Logic - and Back

BRICS Report Series, 1995

One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient model-checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real-time automata using the region-techniques of Alur and Dill. In this paper, we continue this transfer of existing techniques from the setting of finite (untimed) automata to that of timed automata. In particular, a timed logic L ν is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L ν formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L ν with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time 1. * This work has been supported by the European Communities under CONCUR2, BRA 7166 † Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 An exception occurs in Alur's thesis [Alu91] in which a decidability result is presented for a linear timed logic called MITL.

Dynamic controllability via Timed Game Automata

Acta Informatica, 2016

Temporal networks are data structures for representing and reasoning about temporal constraints on activities. Many kinds of temporal networks have been defined in the literature, differing in their expressiveness. The simplest kinds of networks have polynomial algorithms for determining their temporal consistency or different levels of controllability, but corresponding algorithms for more expressive networks (e.g., those that include observation nodes or disjunctive constraints) have so far been unavailable. This paper introduces a new approach to determine the dynamic controllability of a very expressive class of temporal networks that accommodates observation nodes and disjunctive constraints. The approach is based on encoding the dynamic controllability problem into a reachability game for Timed Game Automata (TGAs). This is the first sound and complete approach for determining the dynamic controllability of such networks. The encoding also highlights the theoretical relationships between various kinds of temporal networks and TGAs. The new algorithms have immediate applications in the design and analysis of workflow models being developed to automate business processes, including workflows in the health-care domain. This paper is an extended version of two earlier papers [9,10].

Stochastic games for verification of probabilistic timed automata

2009

Probabilistic timed automata (PTAs) are used for formal modelling and verification of systems with probabilistic, nondeterministic and real-time behaviour. For non-probabilistic timed automata, forwards reachability is the analysis method of choice, since it can be implemented extremely efficiently. However, for PTAs, such techniques are only able to compute upper bounds on maximum reachability probabilities. In this paper, we propose a new approach to the analysis of PTAs using abstraction and stochastic games. We show how efficient forwards reachability techniques can be extended to yield both lower and upper bounds on maximum (and minimum) reachability probabilities. We also present abstraction-refinement techniques that are guaranteed to improve the precision of these probability bounds, providing a fully automatic method for computing the exact values. We have implemented these techniques and applied them to a set of large case studies. We show that, in comparison to alternative approaches to verifying PTAs, such as backwards reachability and digital clocks, our techniques exhibit superior performance and scalability.

Competitive Optimisation on Timed Automata

2009

Page 1. COMPETITIVE OPTIMISATION ON TIMED AUTOMATA BY ASHUTOSH TRIVEDI A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN COMPUTER SCIENCE UNIVERSITY OF WARWICK, DEPARTMENT OF COMPUTER SCIENCE APRIL 2009 Page 2. To Tiziana, for maximising happiness and minimising troubles, and to Miralisa, for playing two-player zero-sum games with me. Page 3.

Dense real-time games

2002

The rapid development of complex and safety-critical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a two-player game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on real-time systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branching-time temporal logic TCTL. While timed games have been studied in the literature, timed games with dense-time winning conditions constitute a new research topic. The main result of this paper is an exponential-time algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable.

Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Lecture Notes in Computer Science, 2010

We consider two-player stochastic games over real-time probabilistic processes where the winning objective is specified by a timed automaton. The goal of player is to play in such a way that the play (a timed word) is accepted by the timed automaton with probability one. Player aims at the opposite. We prove that whenever player has a winning strategy, then she also has a strategy that can be specified by a timed automaton. The strategy automaton reads the history of a play, and the decisions taken by the strategy depend only on the region of the resulting configuration. We also give an exponential-time algorithm which computes a winning timed automaton strategy if it exists.

Game-Theoretic Automata: Foundations, Formalizations, and Open Problems

Game-Theoretic Automata (GTA) unify game theory and automata theory into a single framework, enabling rigorous formalization of sequential games. By leveraging temporal logic, state transitions, and explicit strategy modeling, GTA is both expressive and computationally tractable for a wide range of games. In this paper, we build on established formalisms, including the FuturLang approach to encoding strategic interactions, and introduce a series of open problems-formalized as conjectured theorems-that chart a path toward a deeper theoretical understanding of GTAs. We highlight directions that have broad implications across game theory, automata theory, and AI.