Two-Player Reachability-Price Games on Single-Clock Timed Automata

Abstract

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

A Faster Algorithm for Solving One-Clock Priced Timed Games

“…Priced timed automata and priced timed games are classes of one-player and two-player zero-sum real-time games played on finite graphs that were defined and thoroughly studied in previous works [2,4,3,17,1,7,9,6,8,12,15]. Synthesizing (near-)optimal strategies for priced timed games has many practical applications in embedded systems design; we refer to the cited papers for references.…”

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

“…Finally, studies on quantitative game theory and related algorithms for determining the optimal strategies [26,118,122,25,14,37,99], conducted for various formalisms, like, e.g., automata, are particularly relevant, as such games can be used as models to define the interaction between a system and its environment on the base of quantitative objectives and behaviours inducing costs, rewards, and resource consumption. The relation with model checking is strict, as also demonstrated by the most recent advances in tools like, e.g., PRISM and MCMAS, implementing model checking algorithms for MDPs founded on game semantics.…”

One-Clock Priced Timed Games are PSPACE-hard

“…A state is urgent if the player is not allowed to wait at the state. Urgent states are relevant because the results of [11,20] are based on the technique of converting more and more states into urgent states, since it is easy to solve a game in which all states are urgent.…”

“…As shown in [15], improving on [11,20], the number of event points is less than 12 n for SPTGs and it is less than m • 12 n • poly(n) for OCPTGs. The optimal strategies for SPTGs constructed by [15] have the set of change points being equal to the set of event points.…”

“…In this paper, we focus on the case in which there is exactly one clock, and so we study one-clock priced timed games (OCPTG). It has been shown that one-clock priced timed games always have a value [11], and moreover algorithms have been proposed [11,15,20] for computing the value of these games. The current state of the art is the algorithm of Hansen, Ibsen-Jensen, and Miltersen [15], who give an algorithm that runs in O(m • poly(n) • 12 n ) time, where m is the number of edges and n is the number of vertices.…”