Incremental Realization of Safety Requirements: Non-determinism vs. Modularity

Abstract

This paper investigates the impact of non-determinism and modularity on the complexity of incremental incorporation of safety requirements while preserving liveness (a.k.a. the problem of incremental synthesis). Previous work shows that realizing safety in non-deterministic programs under limited observability is an NP-complete problem (in the state space of the program), where limited observability imposes read restrictions on program components with respect to the local state of other components. In this paper, we present a surprising result that synthesizing safety remains an NP-complete problem even for deterministic programs! The results of this paper imply that non-determinism is not the source of the hardness of synthesizing safety in concurrent programs; instead, limited observability has a major impact on the complexity of realizing safety. We also provide a roadmap for future research on exploiting the benefits of modularization while keeping the complexity of incremental synthesis manageable.