An Agda Formalization of Üresin &amp; Dubois’ Asynchronous Fixed-Point Theory

Zmigrod, Ran; Daggitt, Matthew L.; Griffin, Timothy G.

doi:10.1007/978-3-319-94821-8_37

Cited by 2 publications

(2 citation statements)

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“…This paper is a revised version of our ITP 2018 conference paper [23]. In particular, the following contributions are new: (i) showing that it is possible to enlarge the set of schedules that the iteration converges over, (ii) relaxing the ACO conditions.…”

Section: Contributionsmentioning

confidence: 99%

A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

2019

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Üresin and Dubois' paper "Parallel Asynchronous Algorithms for Discrete Data" shows how a class of synchronous iterative algorithms may be transformed into asynchronous iterative algorithms. They then prove that the correctness of the resulting asynchronous algorithm can be guaranteed by reasoning about the synchronous algorithm alone. These results have been used to prove the correctness of various distributed algorithms, including in the fields of routing, numerical analysis and peer-to-peer protocols. In this paper we demonstrate several ways in which the assumptions that underlie this theory may be relaxed. Amongst others, we (i) expand the set of schedules for which the asynchronous iterative algorithm is known to converge and (ii) weaken the conditions that users must prove to hold to guarantee convergence. Furthermore, we demonstrate that two of the auxiliary results in the original paper are incorrect, and explicitly construct a counterexample. Finally, we also relax the alternative convergence conditions proposed by Gurney based on ultrametrics. Many of these relaxations and errors were uncovered after formalising the work in the proof assistant Agda. This paper describes the Agda code and the library that has resulted from this work. It is hoped that the library will be of use to others wishing to formally verify the correctness of asynchronous iterative algorithms.

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Section: Contributionsmentioning

confidence: 99%

A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

2019

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“…Our Agda formalisation [6] covers ( ), ( ) and ( ). See [30] for a discussion of our formalisation of ( ) and ( ). theory of Üresin & Dubois and Gurney, and we discuss this preparatory work in [30].…”

Section: Our Contributionsmentioning

confidence: 99%

Asynchronous convergence of policy-rich distributed bellman-ford routing protocols

Daggitt

Gurney

Griffin

2018

Proceedings of the 2018 Conference of the ACM Special Interest Group on Data Communication

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We present new results in the theory of asynchronous convergence for the Distributed Bellman-Ford (DBF) family of routing protocols which includes distance-vector protocols (e.g. RIP) and path-vector protocols (e.g. BGP). We take the "increasing" conditions of Sobrinho and make three main new contributions.First, we show that the conditions are sufficient to guarantee that the protocols will converge to a unique solution from any state. This eliminates the possibility of BGP wedgies. Second, unlike previous work, we decouple the computation from the asynchronous context in which it occurs, allowing us to reason about a more relaxed model of asynchronous computation in which routing messages can be lost, reordered, and duplicated. Third, our theory and results have been fully formalised in the Agda theorem prover and the resulting library is publicly available for others to use and extend. We feel this is in line with the increased emphasis on formal verification of software for critical infrastructure.

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An Agda Formalization of Üresin & Dubois’ Asynchronous Fixed-Point Theory

Cited by 2 publications

References 22 publications

A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

Asynchronous convergence of policy-rich distributed bellman-ford routing protocols

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