Synthesis of Strategies Using the Hoare Logic of Angelic and Demonic Nondeterminism

TL;DR

This paper develops a propositional Hoare logic framework for reasoning about programs with both angelic and demonic nondeterminism, enabling compositional analysis and synthesis of correct programs.

Contribution

It introduces a sound and complete Hoare calculus for dual nondeterminism, extending safety game formalism, and analyzes its exponential-time computational complexity.

Findings

The logic is compositional and subsumes safety games.

The calculus is sound and complete for partial correctness.

The theory is complete for exponential time.

Abstract

We study a propositional variant of Hoare logic that can be used for reasoning about programs that exhibit both angelic and demonic nondeterminism. We work in an uninterpreted setting, where the meaning of the atomic actions is specified axiomatically using hypotheses of a certain form. Our logical formalism is entirely compositional and it subsumes the non-compositional formalism of safety games on finite graphs. We present sound and complete Hoare-style calculi that are useful for establishing partial-correctness assertions, as well as for synthesizing implementations. The computational complexity of the Hoare theory of dual nondeterminism is investigated using operational models, and it is shown that the theory is complete for exponential time.