Mechanizing a Process Algebra for Network Protocols

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in Isabelle/HOL is relatively standard, but its layered structure necessitates special treatment. The control states of reactive processes, such as nodes in a network, are modelled by terms of the process algebra. We propose a technique based on these terms to streamline proofs of inductive invariance. This is not sufficient, however, to state and prove invariants that relate states across multiple processes (entire networks). To this end, we propose a novel compositional technique for lifting global invariants stated at the level of individual nodes to networks of nodes.Comment: This paper is an extended version of arXiv:1407.3519. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AWN.shtm

On computing joint invariants of vector fields

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}

A mechanized proof of loop freedom of the (untimed) AODV routing protocol

The Ad hoc On-demand Distance Vector (AODV) routing protocol allows the nodes in a Mobile Ad hoc Network (MANET) or a Wireless Mesh Network (WMN) to know where to forward data packets. Such a protocol is 'loop free' if it never leads to routing decisions that forward packets in circles. This paper describes the mechanization of an existing pen-and-paper proof of loop freedom of AODV in the interactive theorem prover Isabelle/HOL. The mechanization relies on a novel compositional approach for lifting invariants to networks of nodes. We exploit the mechanization to analyse several improvements of AODV and show that Isabelle/HOL can re-establish most proof obligations automatically and identify exactly the steps that are no longer valid.Comment: The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AODV.shtm