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.CCC.2018.15
URN: urn:nbn:de:0030-drops-88747
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8874/
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Edmonds, Jeff ; Medabalimi, Venkatesh ; Pitassi, Toniann

Hardness of Function Composition for Semantic Read once Branching Programs

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LIPIcs-CCC-2018-15.pdf (0.6 MB)

Abstract

In this work, we study time/space trade-offs for function composition. We prove asymptotically optimal lower bounds for function composition in the setting of nondeterministic read once branching programs, for the syntactic model as well as the stronger semantic model of read-once nondeterministic computation. We prove that such branching programs for solving the tree evaluation problem over an alphabet of size k requires size roughly k^{Omega(h)}, i.e space Omega(h log k). Our lower bound nearly matches the natural upper bound which follows the best strategy for black-white pebbling the underlying tree. While previous super-polynomial lower bounds have been proven for read-once nondeterministic branching programs (for both the syntactic as well as the semantic models), we give the first lower bounds for iterated function composition, and in these models our lower bounds are near optimal.

BibTeX - Entry

@InProceedings{edmonds_et_al:LIPIcs:2018:8874,
  author =	{Jeff Edmonds and Venkatesh Medabalimi and Toniann Pitassi},
  title =	{{Hardness of Function Composition for Semantic Read once Branching Programs}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Rocco A. Servedio},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2018/8874},
  URN =		{urn:nbn:de:0030-drops-88747},
  doi =		{10.4230/LIPIcs.CCC.2018.15},
  annote =	{Keywords: Branching Programs, Function Composition, Time-Space Tradeoffs, Semantic Read Once, Tree Evaluation Problem}
}

Keywords: Branching Programs, Function Composition, Time-Space Tradeoffs, Semantic Read Once, Tree Evaluation Problem
Collection: 33rd Computational Complexity Conference (CCC 2018)
Issue Date: 2018
Date of publication: 04.06.2018

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