On the reaction time of some synchronous systems

This paper presents an investigation of the notion of reaction time in some synchronous systems. A state-based description of such systems is given, and the reaction time of such systems under some classic composition primitives is studied. Reaction time is shown to be non-compositional in general. Possible solutions are proposed, and applications to verification are discussed. This framework is illustrated by some examples issued from studies on real-time embedded systems.Comment: In Proceedings ICE 2011, arXiv:1108.014

*-autonomous categories, Unique decomposition categories.

We analyze the categorical foundations of Girard’s Geometry of Interaction Program for Linear Logic. The motivation for the work comes from the importance of viewing GoI as a new kind of semantics and thus trying to relate it to extant semantics. In an earlier paper we showed that a special case of Abramsky’s GoI situations–ones based on Unique Decomposition Categories (UDC’s)–exactly captures Girard’s functional analytic models in his first GoI paper, including Girard’s original Execution formula in Hilbert spaces, his notions of orthogonality, types, datum, algorithm, etc. Here we associate to a UDC-based GoI Situation a denotational model (a ∗-autonomous category (without units) with additional exponential structure). We then relate this model to some of the standard GoI models via a fully-faithful embedding into a double-gluing category, thus connecting up GoI with earlier Full Completenes

A categorical model for the Geometry of Interaction

We consider the multiplicative and exponential fragment of linear logic (MELL) and give a Geometry of Interaction (GoI) semantics for it based on unique decomposition categories. We prove a Soundness and Finiteness Theorem for this interpretation. We show that Girard’s original approach to GoI 1 via operator algebras is exactly captured in this categorical framework

Proofs as Polynomials

Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can b