Expressivity of Time-Varying Graphs View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2013

AUTHORS

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

ABSTRACT

We prove that the set of languages \({\cal L}_{nowait}\) when no waiting is allowed contains all computable languages. On the other end, using algebraic properties of quasi-orders, we prove that \({\cal L}_{wait}\) 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 \({\cal L}_{wait[d]} = {\cal L}_{nowait}\); that is, the complexity of the accepting automaton decreases only if waiting is unbounded. More... »

PAGES

95-106

References to SciGraph publications

Book

TITLE

Fundamentals of Computation Theory

ISBN

978-3-642-40163-3
978-3-642-40164-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-40164-0_12

DOI

http://dx.doi.org/10.1007/978-3-642-40164-0_12

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046900138


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