Cantor meets Scott: Semantic Foundations for Probabilistic Networks

TL;DR

This paper introduces a domain-theoretic semantics for ProbNetKAT, enabling effective approximation and implementation of probabilistic network programs for analyzing network behavior and routing schemes.

Contribution

It provides a novel domain-theoretic characterization of ProbNetKAT's semantics, facilitating practical approximation and implementation of probabilistic network analysis.

Findings

Prototype implementation for ProbNetKAT semantics

Approximate arbitrary ProbNetKAT programs with finite distributions

Applied to network congestion and reachability analysis

Abstract

ProbNetKAT is a probabilistic extension of NetKAT with a denotational semantics based on Markov kernels. The language is expressive enough to generate continuous distributions, which raises the question of how to compute effectively in the language. This paper gives an new characterization of ProbNetKAT's semantics using domain theory, which provides the foundation needed to build a practical implementation. We show how to use the semantics to approximate the behavior of arbitrary ProbNetKAT programs using distributions with finite support. We develop a prototype implementation and show how to use it to solve a variety of problems including characterizing the expected congestion induced by different routing schemes and reasoning probabilistically about reachability in a network.