2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2017)

Reykjavik, Iceland

June 20, 2017 to June 23, 2017

ISBN: 978-1-5090-3019-4

pp: 1-12

Michael Benedikt , Department of Computer Science, University of Oxford, UK

Timothy Duff , School of Mathematics, Georgia Institute of Technology, USA

Aditya Sharad , Department of Computer Science, University of Oxford, UK

James Worrell , Department of Computer Science, University of Oxford, UK

ABSTRACT

We introduce a generalisation of weighted automata over a field, called polynomial automata, and we analyse the complexity of the Zeroness Problem in this model, that is, whether a given automaton outputs zero on all words. While this problem is non-primitive recursive in general, we highlight a subclass of polynomial automata for which the Zeroness Problem is primitive recursive. Refining further, we identify a subclass of affine VAS for which coverability is in 2EXPSPACE. We also use polynomial automata to obtain new proofs that equivalence of streaming string transducers is decidable, and that equivalence of copyless streaming string transducers is in PSPACE.

INDEX TERMS

Automata, Transducers, Complexity theory, Petri nets, Upper bound, Registers, Standards

CITATION

M. Benedikt, T. Duff, A. Sharad and J. Worrell, "Polynomial automata: Zeroness and applications,"

*2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)*, Reykjavik, Iceland, 2017, pp. 1-12.

doi:10.1109/LICS.2017.8005101

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