License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.24
URN: urn:nbn:de:0030-drops-80661
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8066/
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Allender, Eric ; Krebs, Andreas ; McKenzie, Pierre

Better Complexity Bounds for Cost Register Automata

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LIPIcs-MFCS-2017-24.pdf (0.5 MB)

Abstract

Cost register automata (CRAs) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the tropical semiring (N U {infinity},\min,+) can simulate polynomial time computation, proving along the way that a naturally defined width-k circuit value problem over the tropical semiring is P-complete.
Then the copyless variant of the CRA, requiring that semiring operations be applied to distinct registers, is shown no more powerful than NC^1 when the semiring is (Z,+,x) or (Gamma^*,max,concat). This relates questions left open in recent work on the complexity of CRA-computable functions to long-standing class separation conjectures in complexity theory, such as NC versus P and NC^1 versus GapNC^1.

BibTeX - Entry

@InProceedings{allender_et_al:LIPIcs:2017:8066,
  author =	{Eric Allender and Andreas Krebs and Pierre McKenzie},
  title =	{{Better Complexity Bounds for Cost Register Automata}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8066},
  URN =		{urn:nbn:de:0030-drops-80661},
  doi =		{10.4230/LIPIcs.MFCS.2017.24},
  annote =	{Keywords: computational complexity, cost registers}
}

Keywords: computational complexity, cost registers
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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