Symbolic BDD and ADD Algorithms for Energy Games

Abstract

Energy games, which model quantitative consumption of a limited resource, e.g., time or energy, play a central role in quantitative models for reactive systems. Reactive synthesis constructs a controller which satisfies a given specification, if one exists. For energy games a synthesized controller ensures to satisfy not only the safety constraints of the specification but also the quantitative constraints expressed in the energy game. A symbolic algorithm for energy games, recently presented by Chatterjee et al., is symbolic in its representation of quantitative values but concrete in the representation of game states and transitions. In this paper we present an algorithm that is symbolic both in the quantitative values and in the underlying game representation. We have implemented our algorithm using two different symbolic representations for reactive games, Binary Decision Diagrams (BDD) and Algebraic Decision Diagrams (ADD). We investigate the commonalities and differences of the two implementations and compare their running times on specifications of energy games.