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Electronic Colloquium on Computational Complexity

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All reports by Author A. Pavan:

TR21-043 | 15th March 2021
Peter Dixon, A. Pavan, N. V. Vinodchandran

Promise Problems Meet Pseudodeterminism

The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a pseudodeterministic approximation algorithm for this problem: a probabilistic polynomial-time algorithm that outputs a canonical approximation with high ... more >>>

TR19-091 | 7th July 2019
Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, A. Pavan, N. V. Vinodchandran, Osamu Watanabe

A Sublinear-space and Polynomial-time Separator Algorithm for Planar Graphs

In [12] (CCC 2013), the authors presented an algorithm for the reachability problem over directed planar graphs that runs in polynomial-time and uses $O(n^{1/2+\epsilon})$ space. A critical ingredient of their algorithm is a polynomial-time, $\tldO(\sqrt{n})$-space algorithm to compute a separator of a planar graph. The conference version provided a sketch ... more >>>

TR14-126 | 9th October 2014
Debasis Mandal, A. Pavan, Rajeswari Venugopalan

Separating Cook Completeness from Karp-Levin Completeness under a Worst-Case Hardness Hypothesis

We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a {\em 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 ... more >>>

TR14-035 | 13th March 2014
Diptarka Chakraborty, A. Pavan, Raghunath Tewari, N. V. Vinodchandran, Lin Yang

New Time-Space Upperbounds for Directed Reachability in High-genus and $H$-minor-free Graphs.

We obtain the following new simultaneous time-space upper bounds for the directed reachability problem.
(1) A polynomial-time,
$\tilde{O}(n^{2/3}g^{1/3})$-space algorithm for directed graphs embedded on orientable surfaces of genus $g$. (2) A polynomial-time, $\tilde{O}(n^{2/3})$-space algorithm for all $H$-minor-free graphs given the tree decomposition, and (3) for $K_{3, 3}$-free and ... more >>>

TR10-009 | 13th January 2010
A. Pavan, Raghunath Tewari, N. V. Vinodchandran

On the Power of Unambiguity in Logspace

We report progress on the \NL\ vs \UL\ problem.
\item[-] We show unconditionally that the complexity class $\ReachFewL\subseteq\UL$. This improves on the earlier known upper bound $\ReachFewL \subseteq \FewL$.
\item[-] We investigate the complexity of min-uniqueness - a central
notion in studying the \NL\ vs \UL\ problem.
more >>>

TR09-071 | 1st September 2009
John Hitchcock, A. Pavan, N. V. Vinodchandran

Kolmogorov Complexity in Randomness Extraction

We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity
extractor, thus establishing a fundamental equivalence between two forms of extraction studied in the literature: Kolmogorov extraction
more >>>

TR06-071 | 25th April 2006
John Hitchcock, A. Pavan

Hardness Hypotheses, Derandomization, and Circuit Complexity

We consider hypotheses about nondeterministic computation that
have been studied in different contexts and shown to have interesting

1. The measure hypothesis: NP does not have p-measure 0.

2. The pseudo-NP hypothesis: there is an NP language that can be
distinguished from any DTIME(2^n^epsilon) language by an ... more >>>

TR06-039 | 28th February 2006
John Hitchcock, A. Pavan

Comparing Reductions to NP-Complete Sets

Under the assumption that NP does not have p-measure 0, we
investigate reductions to NP-complete sets and prove the following:

- Adaptive reductions are more powerful than nonadaptive
reductions: there is a problem that is Turing-complete for NP but
not truth-table-complete.

- Strong nondeterministic reductions are more powerful ... more >>>

TR05-105 | 24th September 2005
Lance Fortnow, John Hitchcock, A. Pavan, N. V. Vinodchandran, Fengming Wang

Extracting Kolmogorov Complexity with Applications to Dimension Zero-One Laws

We apply recent results on extracting randomness from independent
sources to ``extract'' Kolmogorov complexity. For any $\alpha,
\epsilon > 0$, given a string $x$ with $K(x) > \alpha|x|$, we show
how to use a constant number of advice bits to efficiently
compute another string $y$, $|y|=\Omega(|x|)$, with $K(y) >
(1-\epsilon)|y|$. ... more >>>

TR05-068 | 7th July 2005
Christian Glaßer, A. Pavan, Alan L. Selman, Liyu Zhang

Redundancy in Complete Sets

We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glasser et al., complete sets for all of the following complexity classes are m-mitotic: ... more >>>

TR05-062 | 17th June 2005
A. Pavan, N. V. Vinodchandran

2-Local Random Reductions to 3-Valued Functions

Yao (in a lecture at DIMACS Workshop on structural complexity and
cryptography) showed that if a language L is 2-locally-random
reducible to a Boolean functio, then L is in PSPACE/poly.
Fortnow and Szegedy quantitatively improved Yao's result to show that
such languages are in fact in NP/poly (Information Processing Letters, ... more >>>

TR05-011 | 21st December 2004
Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

Autoreducibility, Mitoticity, and Immunity

We show the following results regarding complete sets:

NP-complete sets and PSPACE-complete sets are many-one

Complete sets of any level of PH, MODPH, or
the Boolean hierarchy over NP are many-one autoreducible.

EXP-complete sets are many-one mitotic.

NEXP-complete sets are weakly many-one mitotic.

PSPACE-complete sets are weakly Turing-mitotic.

... more >>>

TR04-053 | 17th June 2004
A. Pavan, N. V. Vinodchandran

Polylogarithmic Round Arthur-Merlin Games and Random-Self-Reducibility

We consider Arthur-Merlin proof systems where (a) Arthur is a probabilistic quasi-polynomial time Turing machine
and (AMQ)(b) Arthur is a probabilistic exponential time Turing machine (AME). We prove two new results related to these classes.

more >>>

TR04-025 | 24th January 2004
John Hitchcock, A. Pavan, N. V. Vinodchandran

Partial Bi-Immunity and NP-Completeness

The Turing and many-one completeness notions for $\NP$ have been
previously separated under {\em measure}, {\em genericity}, and {\em
bi-immunity} hypotheses on NP. The proofs of all these results rely
on the existence of a language in NP with almost everywhere hardness.

In this paper we separate the same NP-completeness ... more >>>

TR04-019 | 15th January 2004
Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta

Properties of NP-Complete Sets

We study several properties of sets that are complete for NP.
We prove that if $L$ is an NP-complete set and $S \not\supseteq L$ is a p-selective sparse set, then $L - S$ is many-one-hard for NP. We demonstrate existence of a sparse set $S \in \mathrm{DTIME}(2^{2^{n}})$
such ... more >>>

TR02-005 | 3rd January 2002
A. Pavan, Alan L. Selman

Bi-Immunity Separates Strong NP-Completeness Notions

We prove that if for some epsilon > 0 NP contains a set that is
DTIME(2^{n^{epsilon}})-bi-immune, then NP contains a set that 2-Turing
complete for NP but not 1-truth-table complete for NP. Lutz and Mayordomo
(LM96) and Ambos-Spies and Bentzien (AB00) previously obtained the
same consequence using strong ... more >>>

TR01-032 | 3rd April 2001
A. Pavan, Alan L. Selman

Separation of NP-completeness Notions

We use hypotheses of structural complexity theory to separate various
NP-completeness notions. In particular, we introduce an hypothesis from which we describe a set in NP that is Turing complete but not truth-table complete. We provide fairly thorough analyses of the hypotheses that we introduce. Unlike previous approaches, we ... more >>>

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