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Documents authored by Mandal, Debasis

Document
DOI: 10.4230/LIPIcs.MFCS.2016.31
A Note on the Advice Complexity of Multipass Randomized Logspace

Authors: Peter Dixon, Debasis Mandal, A. Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Investigating the complexity of randomized space-bounded machines that are allowed to make multiple passes over the random tape has been of recent interest. In particular, it has been shown that derandomizing such probabilistic machines yields a weak but new derandomization of probabilistic time-bounded classes. In this paper we further explore the complexity of such machines. In particular, as our main result we show that for any epsilon<1, every language that is accepted by an O(n^epsilon)-pass, randomized logspace machine can be simulated in deterministic logspace with linear amount of advice. This result extends an earlier result of Fortnow and Klivans who showed that RL is in deterministic logspace with linear advice.
Cite as

Peter Dixon, Debasis Mandal, A. Pavan, and N. V. Vinodchandran. A Note on the Advice Complexity of Multipass Randomized Logspace. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 31:1-31:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{dixon_et_al:LIPIcs.MFCS.2016.31,
  author =	{Dixon, Peter and Mandal, Debasis and Pavan, A. and Vinodchandran, N. V.},
  title =	{{A Note on the Advice Complexity of Multipass Randomized Logspace}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{31:1--31:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.31},
  URN =		{urn:nbn:de:0030-drops-65003},
  doi =		{10.4230/LIPIcs.MFCS.2016.31},
  annote =	{Keywords: space-bounded computations, randomized machines, advice}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.445
Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis

Authors: Debasis Mandal, A. Pavan, and Rajeswari Venugopalan

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a worst-case hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time O(2^2^n^c) (for some c > 1) accepting Sigma^* whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2^2^{beta * 2^n^c) (for some beta > 0). This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis.
Cite as

Debasis Mandal, A. Pavan, and Rajeswari Venugopalan. Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 445-456, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{mandal_et_al:LIPIcs.FSTTCS.2014.445,
  author =	{Mandal, Debasis and Pavan, A. and Venugopalan, Rajeswari},
  title =	{{Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{445--456},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.445},
  URN =		{urn:nbn:de:0030-drops-48621},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.445},
  annote =	{Keywords: Cook reduction, Karp reduction, NP-completeness, Turing completeness, many-one completeness}
}
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