Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets

Abstract

Abstract. We introduce and study hybrid automata with strong resets. They generalize o-minimal hybrid automata, a class of hybrid automata which allows modeling of complex continuous dynamics. A number of analysis problems, such as reachability testing and controller synthesis, are decidable for classes of ominimal hybrid automata. We generalize existing decidability results for controller synthesis on hybrid automata and we establish new ones by proving that average-price and reachability-price games on hybrid systems with strong resets are decidable, provided that the structure on which the hybrid automaton is defined has a decidable first-order theory. Our proof techniques include a novel characterization of values in games on hybrid systems by optimality equations, and a definition of a new finitary equivalence relation on the states of a hybrid system which enables a reduction of games on hybrid systems to games on finite graphs.

Average-Price-per-Reward Games on Hybrid Automata with Strong Resets

“…Reachability [2][3][4][5] and optimal reachability [6,7] analysis for hybrid automata have been studied. In [6,8] the optimality of infinite behaviours is also addressed.…”

“…In [8] timed automata, a different class of hybrid automata, is considered, and an abstraction technique, known as "corner-point abstraction", is used. We, on the other hand, use an abstraction, that was first proposed in [6], to reduce to price-reward graphs, that are introduced in this paper.…”

“…To reduce hybrid average-price-per-reward games to their counterparts on PRGs we use the same equivalence as in [6]. However, there are two significant contributions with respect to [6].…”

“…However, there are two significant contributions with respect to [6]. Firstly, we are considering the average priceover-reward ratio, whereas only average price per transition was considered in [6].…”

“…To characterise game values we use a technique, referred to as optimality equations [14,6]. What is novel is that we use the values of edge games to express optimality criteria in these equations.…”