4 research outputs found
Synthesis of Strategies and the Hoare Logic of Angelic Nondeterminism
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 mean-ing of the atomic actions is specified axiomatically using hypotheses of a certain form. Our logical formalism is entirely compositional and it sub-sumes 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 synthesiz-ing 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.
Cinnamons: A Computation Model Underlying Control Network Programming
We give the easily recognizable name "cinnamon" and "cinnamon programming" to
a new computation model intended to form a theoretical foundation for Control
Network Programming (CNP). CNP has established itself as a programming paradigm
combining declarative and imperative features, built-in search engine, powerful
tools for search control that allow easy, intuitive, visual development of
heuristic, nondeterministic, and randomized solutions. We define rigorously the
syntax and semantics of the new model of computation, at the same time trying
to keep clear the intuition behind and to include enough examples. The
purposely simplified theoretical model is then compared to both WHILE-programs
(thus demonstrating its Turing-completeness), and the "real" CNP. Finally,
future research possibilities are mentioned that would eventually extend the
cinnamon programming into the directions of nondeterminism, randomness, and
fuzziness.Comment: 7th Intl Conf. on Computer Science, Engineering & Applications
(ICCSEA 2017) September 23~24, 2017, Copenhagen, Denmar
Synthesis of Strategies Using the Hoare Logic of Angelic and Demonic 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 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
Extracting total Amb programs from proofs
We present a logical system CFP (Concurrent Fixed Point Logic) supporting the
extraction of nondeterministic and concurrent programs that are provably total
and correct. CFP is an intuitionistic first-order logic with inductive and
coinductive definitions extended by two propositional operators: Rrestriction,
a strengthening of implication, and an operator for total concurrency. The
source of the extraction are formal CFP proofs, the target is a lambda calculus
with constructors and recursion extended by a constructor Amb (for McCarthy's
amb) which is interpreted operationally as globally angelic choice and is used
to implement nondeterminism and concurrency. The correctness of extracted
programs is proven via an intermediate domain-theoretic denotational semantics.
We demonstrate the usefulness of our system by extracting a nondeterministic
program that translates infinite Gray code into the signed digit
representation. A noteworthy feature of CFP is the fact that the proof rules
for restriction and concurrency involve variants of the classical law of
excluded middle that would not be interpretable computationally without Amb.Comment: 39 pages + 4 pages appendix. arXiv admin note: text overlap with
arXiv:2104.1466