Constructive Hybrid Games

Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where proofs that a player can win the game correspond to computable winning strategies. This is the logical foundation for synthesis of correct control and monitoring code for safety-critical cyber-physical systems. Our contributions include novel static and dynamic semantics as well as soundness and consistency.Comment: 60 pages, preprint, under revie

Probabilistic NetKAT

Contains fulltext : 143761.pdf (publisher's version ) (Open Access)19 p

Nominal Kleene coalgebra

Contains fulltext : 141320.pdf (preprint version ) (Open Access)1 p

Completeness and incompleteness in nominal Kleene algebra

Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with statically scoped allocation of resources, along with a semantics consisting of nominal languages. They also provided an axiomatization that captures the behavior of the scoping operator and its interaction with the Kleene algebra operators and proved soundness over nominal languages. In this paper, we show that the axioms proposed by Gabbay and Ciancia are not complete over the semantic interpretation they propose. We then identify a slightly wider class of language models over which they are sound and complete