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.2018.51
URN: urn:nbn:de:0030-drops-96330
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9633/
Hemaspaandra, Edith ;
Hemaspaandra, Lane A. ;
Spakowski, Holger ;
Watanabe, Osamu
The Robustness of LWPP and WPP, with an Application to Graph Reconstruction
Abstract
We show that the counting class LWPP [S. Fenner et al., 1994] remains unchanged even if one allows a polynomial number of gap values rather than one. On the other hand, we show that it is impossible to improve this from polynomially many gap values to a superpolynomial number of gap values by relativizable proof techniques.
The first of these results implies that the Legitimate Deck Problem (from the study of graph reconstruction) is in LWPP (and thus low for PP, i.e., PP^{Legitimate Deck} = PP) if the weakened version of the Reconstruction Conjecture holds in which the number of nonisomorphic preimages is assumed merely to be polynomially bounded. This strengthens the 1992 result of Köbler, Schöning, and Torán [J. Köbler et al., 1992] that the Legitimate Deck Problem is in LWPP if the Reconstruction Conjecture holds, and provides strengthened evidence that the Legitimate Deck Problem is not NP-hard.
We additionally show on the one hand that our main LWPP robustness result also holds for WPP, and also holds even when one allows both the rejection- and acceptance- gap-value targets to simultaneously be polynomial-sized lists; yet on the other hand, we show that for the #P-based analog of LWPP the behavior much differs in that, in some relativized worlds, even two target values already yield a richer class than one value does.
BibTeX - Entry
@InProceedings{hemaspaandra_et_al:LIPIcs:2018:9633,
author = {Edith Hemaspaandra and Lane A. Hemaspaandra and Holger Spakowski and Osamu Watanabe},
title = {{The Robustness of LWPP and WPP, with an Application to Graph Reconstruction}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {51:1--51:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Igor Potapov and Paul Spirakis and James Worrell},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9633},
URN = {urn:nbn:de:0030-drops-96330},
doi = {10.4230/LIPIcs.MFCS.2018.51},
annote = {Keywords: structural complexity theory, robustness of counting classes, the legitimate deck problem, PP-lowness, the Reconstruction Conjecture}
}
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Keywords: |
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structural complexity theory, robustness of counting classes, the legitimate deck problem, PP-lowness, the Reconstruction Conjecture |
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Collection: |
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43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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27.08.2018 |
