Average-energy games

In reactive controller synthesis, a number of implementations (controllers) are possible for a given specification because of incomplete nature of specification. To choose the most desirable one from the various options, we need to specify additional properties which can guide the synthesis. In this paper, We propose a technique for guided controller synthesis from regular requirements which are specified using an interval temporal logic QDDC. We find that QDDC is well suited for guided synthesis due to its superiority in dealing with both qualitative and quantitative specifications. Our framework allows specification consisting of both hard and soft requirements as QDDC formulas. We have also developed a method and a tool DCSynth, which computes a controller that invariantly satisfies the hard requirement and it optimally meets the soft requirement. The proposed technique is also useful in dealing with conflicting i.e., unrealizable requirements, by making some of the them as soft requirements. Case studies are carried out to demonstrate the effectiveness of the soft requirement guided synthesis in obtaining high quality controllers. The quality of the synthesized controllers is compared using metrics measuring both the guaranteed and the expected case behaviour of the controlled system. Tool DCSynth facilitates such comparison. This paper introduces a tool DCSynth which allows synthesis of controllers from regular properties (QDDC formulas). The specification in DCSynth is a tuple (I, O, D h , D s ), where D h and D s are QDDC formulas over a set of input and output propositions (I, O). Here, D h and D s are the hard and the soft requirement, respectively 1 . We use the term supervisor for a non-blocking Mealy machine which may non-deterministically produce one or more outputs for each input. A supervisor may be refined to a sub-supervisor by resolving (pruning) the non-determinstic choice of outputs (the sub-supervisor may use additional memory for making the choice.) We define a determinism ordering on supervisors in the paper. A controller is a deterministic supervisor. Ramadge and Wonham [25,26] investigated the synthesis of the maximally permissive supervisor for a regular specification. The maximally permissive supervisor is a unique supervisor, which encompasses all the behaviors invariantly satisfying the specified regular property (See Definition 6). The well known safety synthesis algorithm applied to the DFA for D h gives us the maximally permissive supervisor M P S(D h ) [10]. If no such supervisor exists, the specification is reported as unrealizable.Any controller obtained by arbitrarily resolving the nondeterministic choices for outputs in M P S(D h ) is correct-by-construction. This results in several controllers with distinct behaviours (as shown by previous example). Thus, only correct-by-construction synthesis is not sufficient [3]. Some form of guidance must be provided to the synthesis method to choose among the possible controllers. We use the soft requirements to provide such guidance. Ou...

Section: Experimental Evaluationmentioning

confidence: 99%

“…Synthesis from Mine-pump(8,2,6,2) and Arb(5,3,2) specifications in DCSynth. The last column gives the expected value of commitment in long run on random inputs.…”

mentioning

confidence: 99%

DCSynth: Guided Reactive Synthesis with Soft Requirements

Wakankar

Pandya

Matteplackel

2020

“…The problem has since been shown to be undecidable for games with three or more clocks [17,10]. Priced timed games have recently been extended to allow partial observability [18] and to energy games [14].…”

Section: Introductionmentioning

confidence: 99%

Verification and Control of Turn-Based Probabilistic Real-Time Games

Kwiatkowska

Norman

Parker

2019

Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative aspects of system behaviour, for example safety, reliability and performance, or to help synthesise controllers that ensure such guarantees are met. We propose the model of turn-based probabilistic timed multi-player games, which incorporates probabilistic choice, real-time clocks and nondeterministic behaviour across multiple players. Building on the digital clocks approach for the simpler model of probabilistic timed automata, we show how to compute the key measures that underlie quantitative verification, namely the probability and expected cumulative price to reach a target. We illustrate this on case studies from computer security and task scheduling.

“…The latter requirement reduces the wear and tear of the system, but cannot be expressed as an energy objective nor as a parity objective. Constraints on the long-run average energy level (which exactly represents the amount of oil in our example) can be specified using the average-energy objective [5]. As seen in this example, they are typically studied in conjunction with bounds on the energy level.…”

Section: Introductionmentioning

confidence: 99%

Bounding Average-Energy Games

Bouyer

Hofman

Markey

et al. 2017

Self Cite

Abstract. We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound constraint on the energy level (but no upper bound) remained open; in particular, so far there was no known upper bound on the memory that is required for winning strategies. By reducing average-energy games with lower-bounded energy to infinite-state mean-payoff games and analyzing the density of low-energy configurations, we show an almost tight doubly-exponential upper bound on the necessary memory, and that the winner of average-energy games with lower-bounded energy can be determined in doubly-exponential time. We also prove EXPSPACE-hardness of this problem. Finally, we consider multi-dimensional extensions of all types of average-energy games: without bounds, with only a lower bound, and with both a lower and an upper bound on the energy. We show that the fully-bounded version is the only case to remain decidable in multiple dimensions.