Cooperative Reactive Synthesis

TL;DR

This paper introduces a hierarchy of cooperation levels in reactive system synthesis, enabling the creation of systems that better collaborate with their environment to satisfy specifications, especially in the context of LTL.

Contribution

It proposes a hierarchy of cooperation levels and a synthesis method to achieve the highest cooperation level for LTL specifications, improving system-environment interaction.

Findings

Synthesized systems can reach the highest cooperation levels.

The approach exploits cooperative environment behavior during operation.

Complexity of the synthesis remains doubly-exponential, matching standard LTL synthesis.

Abstract

A modern approach to engineering correct-by-construction systems is to synthesize them automatically from formal specifications. Oftentimes, a system can only satisfy its guarantees if certain environment assumptions hold, which motivates their inclusion in the system specification. Experience with modern synthesis approaches shows that synthesized systems tend to satisfy their specifications by actively working towards the violation of the assumptions rather than satisfying assumptions and guarantees together. Such uncooperative behavior is undesirable because it violates the aim of synthesis: the system should try to satisfy its guarantees and use the assumptions only when needed. Also, the assumptions often describe the valid behavior of other components in a bigger system, which should not be obstructed unnecessarily. In this paper, we present a hierarchy of cooperation levels between system and environment. Each level describes how well the system enforces both the assumptions and guarantees. We show how to synthesize systems that achieve the highest possible cooperation level for a given specification in Linear Temporal Logic (LTL). The synthesized systems can also exploit cooperative environment behavior during operation to reach a higher cooperation level that is not enforceable by the system initially. The worst-case time complexity of our synthesis procedure is doubly-exponential, which matches the complexity of standard LTL synthesis. This is an extended version of [7] that features an additional appendix.