Infinite Networks, Halting and Local Algorithms

Antti Kuusisto

The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms provide a natural framework that could be used in order to theoretically control infinite networks in finite time. We study a comprehensive collection of distributed computing models and prove that if infinite networks are included in the class of structures investigated, then every universally halting distributed algorithm is in fact a local algorithm. To contrast this result, we show that if only finite networks are allowed, then even very weak distributed computing models can define nonlocal algorithms that halt everywhere. The investigations in this article continue the studies in the intersection of logic and distributed computing initiated in (Hella et al., PODC 2012) and (Kuusisto, CSL 2013).

In Adriano Peron and Carla Piazza: Proceedings Fifth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2014), Verona, Italy, 10th - 12th September 2014, Electronic Proceedings in Theoretical Computer Science 161, pp. 147–160.
Published: 24th August 2014.

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