Expressivity of time-varying graphs

Arnaud Casteigts, Paola Flocchini, Emmanuel Godard, Nicola Santoro, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Time-varying graphs model in a natural way infrastructure-less highly dynamic systems, such as wireless ad-hoc mobile networks, robotic swarms, vehicular networks, etc. In these systems, a path from a node to another might still exist over time, rendering computing possible, even though at no time the path exists in its entirety. Some of these systems allow waiting (i.e., provide the nodes with store-carry-forward-like mechanisms such as local buffering) while others do not. In this paper, we focus on the structure of the time-varying graphs modelling these highly dynamical environments. We examine the complexity of these graphs, with respect to waiting, in terms of their expressivity; that is in terms of the language generated by the feasible journeys (i.e., the "paths over time"). We prove that the set of languages Lnowait when no waiting is allowed contains all computable languages. On the other end, using algebraic properties of quasi-orders, we prove that Lwait is just the family of regular languages, even if the presence of edges is controlled by some arbitrary function of the time. In other words, we prove that, when waiting is allowed, the power of the accepting automaton drops drastically from being as powerful as a Turing machine, to becoming that of a Finite-State machine. This large gap provides a measure of the impact of waiting. We also study bounded waiting; that is when waiting is allowed at a node for at most d time units. We prove that Lwait[d] = Lnowait; that is, the complexity of the accepting automaton decreases only if waiting is unbounded.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings
Pages95-106
Number of pages12
DOIs
Publication statusPublished - Sep 3 2013
Event19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom
Duration: Aug 19 2013Aug 21 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8070 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Symposium on Fundamentals of Computation Theory, FCT 2013
CountryUnited Kingdom
CityLiverpool
Period8/19/138/21/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Casteigts, A., Flocchini, P., Godard, E., Santoro, N., & Yamashita, M. (2013). Expressivity of time-varying graphs. In Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings (pp. 95-106). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8070 LNCS). https://doi.org/10.1007/978-3-642-40164-0_12