Abstract
Recently, Dallal, Neider, and Tabuada studied a generalization of the classical game-theoretic model used in program synthesis, which additionally accounts for unmodeled intermittent disturbances. In this extended framework, one is interested in computing optimally resilient strategies, i.e., strategies that are resilient against as many disturbances as possible. Dallal, Neider, and Tabuada showed how to compute such strategies for safety specifications. In this work, we compute optimally resilient strategies for a much wider range of winning conditions and show that they do not require more memory than winning strategies in the classical model. Our algorithms only have a polynomial overhead in comparison to the ones computing winning strategies. In particular, for parity conditions, optimally resilient strategies are positional and can be computed in quasipolynomial time.
Highlights
Reactive synthesis is an exciting and promising approach to solving a crucial problem, whose importance is ever-increasing due to ubiquitous deployment of embedded systems: obtaining correct and verified controllers for safety-critical systems
Reactive synthesis is modeled as a two-player zero-sum game on a finite graph that is played between the system, which seeks to satisfy the specification, and its environment, which seeks to violate it
The assumptions on G that need to be satisfied for Theorem 1 to hold are as follows: 1. The game GU is determined for every U ⊆ V . 2
Summary
Reactive synthesis is an exciting and promising approach to solving a crucial problem, whose importance is ever-increasing due to ubiquitous deployment of embedded systems: obtaining correct and verified controllers for safety-critical systems. Reactive synthesis is modeled as a two-player zero-sum game on a finite graph that is played between the system, which seeks to satisfy the specification, and its environment, which seeks to violate it. This model is well understood, there are still multiple obstacles to overcome before synthesis can be realistically applied in practice. These obstacles include the high computational complexity of the problem, and more fundamental ones. Among the most prohibitive issues in this regard is the need for a complete model of the interaction between the system and its environment, including an accurate model of the environment, the actions available to both players, as well as the effects of these actions
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