Showing Invariance Compositionally for a Process Algebra for Network Protocols

Abstract

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.

Modelling and verifying the AODV routing protocol

“…To increase the level of confidence of our analysis even further, we mechanised AWN as well as the presented pen-and-paper proof of loop freedom of AODV in the interactive theorem prover Isabelle/HOL. [7,6] When verifying our (pen-and-paper) proof we did not find any major errors: (1) type checking found a minor typo in the model, (2) one proof invoked an incorrect invariant requiring the addition and proof of a new invariant based on an existing one, (3) a minor flaw in another proof required the addition of a new invari-26 http://www.ietf.org/iesg/statement/ pseudocode-guidelines.html ant. All these "flaws" have been repaired in the present proof.…”

“…In this paper we abstain from a formal definition of the operational semantics. 7 Instead, we employ a correspondence between the transitions of AWN processes and the execution of actions-subexpressions as occur in Entries 3-10 of Table 1-identified by line numbers in protocol specifications in AWN. 4 R. van Glabbeek, P. Höfner, M. Portmann, W.L.…”

“…AODV(ip , sn , rt , rreqs , store)7.+ [ oip = ip ]/* this node is not the originator; forward RREP */ 8.…”

A Mechanized Proof of Loop Freedom of the (Untimed) AODV Routing Protocol

“…In this paper, however, we focus on an application and mechanize the proof of loop freedom of AODV, a crucial correctness property. Our proof uses standard transition-system based techniques for showing safety properties [15,16], as well as a novel compositional technique for lifting properties from individual nodes to networks of nodes [4]. We demonstrate these techniques on an example of significant size and practical interest.…”

“…By focusing mainly on the application (loop freedom of AODV), we only show a glimpse of our proof method. A companion paper [4] presents the technical details of the mechanization of AWN and the associated framework for compositional proof. Source files of the complete mechanization in Isabelle/HOL are available online [5].…”