Probabilistic Program Equivalence for NetKAT

TL;DR

This paper presents a decision procedure for probabilistic program equivalence in a network programming language, enabling automated verification of network properties using Markov chain semantics.

Contribution

It introduces a novel approach to decide equivalence in Probabilistic NetKAT using stochastic matrices and Markov chains, addressing iteration challenges.

Findings

Decidable for the history-free fragment of Probabilistic NetKAT.

Effective verification of network resilience and failure properties.

Application to real-world data center network case study.

Abstract

We tackle the problem of deciding whether two probabilistic programs are equivalent in Probabilistic NetKAT, a formal language for specifying and reasoning about the behavior of packet-switched networks. We show that the problem is decidable for the history-free fragment of the language by developing an effective decision procedure based on stochastic matrices. The main challenge lies in reasoning about iteration, which we address by designing an encoding of the program semantics as a finite-state absorbing Markov chain, whose limiting distribution can be computed exactly. In an extended case study on a real-world data center network, we automatically verify various quantitative properties of interest, including resilience in the presence of failures, by analyzing the Markov chain semantics.