Synthesis of Strategies and the Hoare Logic of Angelic Nondeterminism
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 (partial-correctness) calculi that are useful for establishing Hoare 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.
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- 2.Celiku, O., Wright, J.v.: Implementing angelic nondeterminism. In: Tenth Asia-Pacific Software Engineering Conference, pp. 176–185 (2003)Google Scholar
- 7.Mamouras, K.: The Hoare logic of deterministic and nondeterministic monadic recursion schemes (2014) (manuscript)Google Scholar
- 8.Mamouras, K.: On the Hoare theory of monadic recursion schemes. In: Proceedings of CSL-LICS (2014)Google Scholar
- 9.Mamouras, K.: Synthesis of strategies using the Hoare logic of angelic and demonic nondeterminism (2015) (in preparation)Google Scholar
- 10.Martin, C.E., Curtis, S.A., Rewitzky, I.: Modelling nondeterminism. In: Mathematics of Program Construction, pp. 228–251 (2004)Google Scholar
- 11.Morgan, C.: Programming From Specifications. Prentice-Hall (1998)Google Scholar