On the capacity of capacitated automata

Orna Kupferman*, Sarai Sheinvald

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Capacitated automata (CAs) have been recently introduced in [8] as a variant of finite-state automata in which each transition is associated with a (possibly infinite) capacity. The capacity bounds the number of times the transition may be traversed in a single run. The study in [8] includes preliminary results about the expressive power of CAs, their succinctness, and the complexity of basic decision problems for them. We continue the investigation of the theoretical properties of CAs and solve problems that have been left open in [8]. In particular, we show that union and intersection of CAs involve an exponential blow-up and that their determinization involves a doubly-exponential blow up. This blow-up is carried over to complementation and to the complexity of the universality and containment problems, which we show to be EXPSPACE-complete. On the positive side, capacities do not increase the complexity when used in the deterministic setting. Also, the containment problem for nondeterministic CAs is PSPACE-complete when capacities are used only in the left-hand side automaton. Our results suggest that while the succinctness of CAs leads to a corresponding increase in the complexity of some of their decision problems, there are also settings in which succinctness comes at no price.

Original languageAmerican English
Title of host publicationLanguage and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings
EditorsBianca Truthe, Jan Janoušek, Adrian-Horia Dediu, Carlos Martín-Vide
PublisherSpringer Verlag
Pages307-319
Number of pages13
ISBN (Print)9783319299990
DOIs
StatePublished - 2016
Event10th International Conference on Language and Automata Theory and Applications, LATA 2016 - Prague, Czech Republic
Duration: 14 Mar 201618 Mar 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9618
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Conference on Language and Automata Theory and Applications, LATA 2016
Country/TerritoryCzech Republic
CityPrague
Period14/03/1618/03/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

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