Bicategorical Semantics for Nondeterministic Computation

We outline a bicategorical syntax for the interaction between public and private information in classical information theory. We use this to give high-level graphical definitions of encrypted communication and secret sharing protocols, including a characterization of their security properties. Remarkably, this makes it clear that the protocols have an identical abstract form to the quantum teleportation and dense coding procedures, yielding evidence of a deep connection between classical and quantum information processing. We also formulate public-key cryptography using our scheme. Specific implementations of these protocols as nondeterministic classical procedures are recovered by applying our formalism in a symmetric monoidal bicategory of matrices of relations.Comment: 21 page

Experiences in porting mini-applications to OpenACC and OpenMP on heterogeneous systems

This article studies mini-applications—Minisweep, GenASiS, GPP, and FF—that use computational methods commonly encountered in HPC. We have ported these applications to develop OpenACC and OpenMP versions, and evaluated their performance on Titan (Cray XK7 with K20x GPUs), Cori (Cray XC40 with Intel KNL), Summit (IBM AC922 with Volta GPUs), and Cori-GPU (Cray CS-Storm 500NX with Intel Skylake and Volta GPUs). Our goals are for these new ports to be useful to both application and compiler developers, to document and describe the lessons learned and the methodology to create optimized OpenMP and OpenACC versions, and to provide a description of possible migration paths between the two specifications. Cases where specific directives or code patterns result in improved performance for a given architecture are highlighted. We also include discussions of the functionality and maturity of the latest compilers available on the above platforms with respect to OpenACC or OpenMP implementations

A Characterization of Consensus Solvability for Closed Message Adversaries

Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430