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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

We study the classical and quantum bit-probe versions of the static set membership problem : Given a subset, S (|S| ≤ n) of a universe, 𝒰 (|𝒰| = m ≫ n), represent it as a binary string in memory so that the query "Is x in S?" (x ∈ 𝒰) can be answered by making at most t probes into the string. Let s_{A}(m,n,t) denote the minimum length of the bit string in any scheme that solves this static set membership problem. We show that for n ≥ 4
s_A(m,n,t = 2) =
𝒪(m^{1-1/(n-1)}) (if n = 0 (mod 3));
𝒪(m^{1-1/n}) (if n = 1,2 (mod 3));
𝒪(m^{6/7}) (if n = 8,9).
These bounds are shown using a common scheme that is based on a graph-theoretic observation on orienting the edges of a graph of high girth. For all n ≥ 4, these bounds substantially improve on the previous best bounds known for this problem, some of which required elaborate constructions [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020]. Our schemes are explicit. A lower bound of the form s_A(m,n,2) = Ω(m^{1-1/⌊{n/4}⌋}) was known for this problem. We show an improved lower bound of s_A(m,n,2) = Ω(m^{1-2/(n+3)}); this bound was previously known only for n = 3,5 [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020; Mirza Galib Anwarul Husain Baig et al., 2019; Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2018; Mirza Galib Anwarul Husain Baig et al., 2019; Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020].
We consider the quantum version of the problem, where access to the bit-string b ∈ {0,1}^s is provided in the form of a quantum oracle that performs the transformation 𝒪_b: |i⟩ ↦ (-1)^{b_i} |i⟩. Let s_Q(m,n,2) denote the minimum length of the bit string that solves the above set membership problem in the quantum model (with adaptive queries but no error). We show that for all n ≤ m^{1/8}, we have s_{QA}(m,n,2) = 𝒪(m^{7/8}). This upper bound makes crucial use of Nash-William’s theorem [Diestel, 2005] for decomposing a graph into forests. This result is significant because, prior to this work, it was not known if quantum schemes yield any advantage over classical schemes. We also consider schemes that make a small number of quantum non-adaptive probes. In particular, we show that the space required in this case, s_{QN}(m,n = 2,t = 2) = O(√m) and s_{QN}(m,n = 2,t = 3) = O(m^{1/3}); in contrast, it is known that two non-adaptive classical probes yield no savings. Our quantum schemes are simple and use only the fact that the XOR of two bits of memory can be computed using just one quantum query to the oracle.

Shyam S. Dhamapurkar, Shubham Vivek Pawar, and Jaikumar Radhakrishnan. Set Membership with Two Classical and Quantum Bit Probes. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 52:1-52:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dhamapurkar_et_al:LIPIcs.ICALP.2022.52, author = {Dhamapurkar, Shyam S. and Pawar, Shubham Vivek and Radhakrishnan, Jaikumar}, title = {{Set Membership with Two Classical and Quantum Bit Probes}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {52:1--52:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.52}, URN = {urn:nbn:de:0030-drops-163932}, doi = {10.4230/LIPIcs.ICALP.2022.52}, annote = {Keywords: set membership problem, bit probe complexity, graphs with high girth, quantum data structure} }

Document

**Published in:** LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

The following is a classical question of Erdős (Nordisk Matematisk Tidskrift, 1963) and of Erdős and Lovász (Colloquia Mathematica Societatis János Bolyai, vol. 10, 1975). Given a hypergraph ℱ with minimum edge-size k, what is the largest function g(k) such that if the expected number of monochromatic edges in ℱ is at most g(k) when the vertices of ℱ are colored red and blue randomly and independently, then we are guaranteed that ℱ is two-colorable? Duraj, Gutowski and Kozik (ICALP 2018) have shown that g(k) ≥ Ω(log k). On the other hand, if ℱ is k-uniform, the lower bound on g(k) is much higher: g(k) ≥ Ω(√{k / log k}) (Radhakrishnan and Srinivasan, Rand. Struct. Alg., 2000). In order to bridge this gap, we define a family of locally-almost-uniform hypergraphs, for which we show, via the randomized algorithm of Cherkashin and Kozik (Rand. Struct. Alg., 2015), that g(k) can be much higher than Ω(log k), e.g., 2^Ω(√{log k}) under suitable conditions.

Jaikumar Radhakrishnan and Aravind Srinivasan. Property B: Two-Coloring Non-Uniform Hypergraphs. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 31:1-31:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{radhakrishnan_et_al:LIPIcs.FSTTCS.2021.31, author = {Radhakrishnan, Jaikumar and Srinivasan, Aravind}, title = {{Property B: Two-Coloring Non-Uniform Hypergraphs}}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)}, pages = {31:1--31:8}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-215-0}, ISSN = {1868-8969}, year = {2021}, volume = {213}, editor = {Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.31}, URN = {urn:nbn:de:0030-drops-155428}, doi = {10.4230/LIPIcs.FSTTCS.2021.31}, annote = {Keywords: Hypergraph coloring, Propery B} }

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**Published in:** LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

We consider the bit-probe complexity of the set membership problem: represent an n-element subset S of an m-element universe as a succinct bit vector so that membership queries of the form "Is x ∈ S" can be answered using at most t probes into the bit vector. Let s(m,n,t) (resp. s_N(m,n,t)) denote the minimum number of bits of storage needed when the probes are adaptive (resp. non-adaptive). Lewenstein, Munro, Nicholson, and Raman (ESA 2014) obtain fully-explicit schemes that show that
s(m,n,t) = 𝒪((2^t-1)m^{1/(t - min{2⌊log n⌋, n-3/2})}) for n ≥ 2,t ≥ ⌊log n⌋+1 .
In this work, we improve this bound when the probes are allowed to be superlinear in n, i.e., when t ≥ Ω(nlog n), n ≥ 2, we design fully-explicit schemes that show that
s(m,n,t) = 𝒪((2^t-1)m^{1/(t-{n-1}/{2^{t/(2(n-1))}})}),
asymptotically (in the exponent of m) close to the non-explicit upper bound on s(m,n,t) derived by Radhakrishan, Shah, and Shannigrahi (ESA 2010), for constant n.
In the non-adaptive setting, it was shown by Garg and Radhakrishnan (STACS 2017) that for a large constant n₀, for n ≥ n₀, s_N(m,n,3) ≥ √{mn}. We improve this result by showing that the same lower bound holds even for storing sets of size 2, i.e., s_N(m,2,3) ≥ Ω(√m).

Palash Dey, Jaikumar Radhakrishnan, and Santhoshini Velusamy. Improved Explicit Data Structures in the Bit-Probe Model Using Error-Correcting Codes. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 28:1-28:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dey_et_al:LIPIcs.MFCS.2020.28, author = {Dey, Palash and Radhakrishnan, Jaikumar and Velusamy, Santhoshini}, title = {{Improved Explicit Data Structures in the Bit-Probe Model Using Error-Correcting Codes}}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, pages = {28:1--28:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-159-7}, ISSN = {1868-8969}, year = {2020}, volume = {170}, editor = {Esparza, Javier and Kr\'{a}l', Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.28}, URN = {urn:nbn:de:0030-drops-126965}, doi = {10.4230/LIPIcs.MFCS.2020.28}, annote = {Keywords: Set membership, Bit-probe model, Fully-explicit data structures, Adaptive data structures, Error-correcting codes} }

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**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs that have k terminal vertices. We show that every interval graph admits a distance-preserving subgraph with O(k log k) branching vertices. We also prove a matching lower bound by exhibiting an interval graph based on bit-reversal permutation matrices. In addition, we show that interval graphs admit subgraphs with O(k) branching vertices that approximate distances up to an additive term of +1.

Kshitij Gajjar and Jaikumar Radhakrishnan. Distance-Preserving Subgraphs of Interval Graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 39:1-39:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gajjar_et_al:LIPIcs.ESA.2017.39, author = {Gajjar, Kshitij and Radhakrishnan, Jaikumar}, title = {{Distance-Preserving Subgraphs of Interval Graphs}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {39:1--39:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.39}, URN = {urn:nbn:de:0030-drops-78798}, doi = {10.4230/LIPIcs.ESA.2017.39}, annote = {Keywords: interval graphs, shortest path, distance-preserving subgraphs, bit-reversal permutation matrix} }

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**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S?" by non-adaptively probing the bit vector at t places. Let s_N(m,n,t) be the minimum number of bits of storage needed for such a scheme. In this work, we show existence of non-adaptive and adaptive schemes for a range of t that improves an upper bound of Buhrman, Miltersen, Radhakrishnan and Srinivasan (2002) on s_N(m,n,t). For three non-adaptive probes, we improve the previous best lower bound on s_N(m,n,3) by Alon and Feige (2009).

Mohit Garg and Jaikumar Radhakrishnan. Set Membership with Non-Adaptive Bit Probes. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{garg_et_al:LIPIcs.STACS.2017.38, author = {Garg, Mohit and Radhakrishnan, Jaikumar}, title = {{Set Membership with Non-Adaptive Bit Probes}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {38:1--38:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.38}, URN = {urn:nbn:de:0030-drops-69952}, doi = {10.4230/LIPIcs.STACS.2017.38}, annote = {Keywords: Data Structures, Bit-probe model, Compression, Bloom filters, Expansion} }

Document

**Published in:** LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

The pointer function of Goos, Pitassi and Watson and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and quantum query complexity, exact and approximate polynomial degree, etc. In particular, Ambainis et al. (STOC 2016) obtained the widest possible (quadratic) separations between deterministic and zero-error randomized query complexity, as well as between bounded-error and zero-error randomized query complexity by considering variants of this pointer function.
However, as Ambainis et al. pointed out in their work, the precise zero-error complexity of the original pointer function was
not known. We show a lower bound of ~Omega(n^{3/4}) on the zero-error randomized query complexity of the pointer function on Theta(n * log(n)) bits; since an ~O(n^{3/4}) upper bound was already shown by Mukhopadhyay and Sanyal (FSTTCS 2015), our lower bound is optimal up to polylog factors. We, in fact, consider a generalization of the original function and obtain lower bounds for it that are optimal up to polylog factors.

Jaikumar Radhakrishnan and Swagato Sanyal. The Zero-Error Randomized Query Complexity of the Pointer Function. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{radhakrishnan_et_al:LIPIcs.FSTTCS.2016.16, author = {Radhakrishnan, Jaikumar and Sanyal, Swagato}, title = {{The Zero-Error Randomized Query Complexity of the Pointer Function}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {16:1--16:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-027-9}, ISSN = {1868-8969}, year = {2016}, volume = {65}, editor = {Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.16}, URN = {urn:nbn:de:0030-drops-68514}, doi = {10.4230/LIPIcs.FSTTCS.2016.16}, annote = {Keywords: Deterministic Decision Tree, Randomized Decision Tree, Query Complexity, Models of Computation.} }

Document

**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Let f: {0,1}^n*{0,1}^n -> {0,1} be a 2-party function. For every product distribution mu on {0,1}^n*{0,1}^n, we show that
CC^{mu}_{0.49}(f) = O(log(prt_{1/8}(f))*log(log(prt_{1/8}(f)))^2),
where CC^{mu}_{epsilon}(f) is the distributional communication complexity of f with error at most epsilon under the distribution mu and prt_{1/8}(f) is the partition bound of f, as defined by Jain and Klauck [Proc. 25th CCC, 2010]. We also prove a similar bound in terms of IC_{1/8}(f), the information complexity of f, namely,
CC^{mu}_{0.49}(f) = O((IC_{1/8}(f)*log(IC_{1/8}(f)))^2).
The latter bound was recently and independently established by Kol [Proc. 48th STOC, 2016] using a different technique.
We show a similar result for query complexity under product distributions. Let g: {0,1}^n -> {0,1} be a function. For every bit-wise product distribution mu on {0,1}^n, we show that
QC^{mu}_{0.49}(g) = O((log(qprt_{1/8}(g))*log(log(qprt_{1/8}(g))))^2),
where QC^{mu}_{epsilon}(g) is the distributional query complexity of f with error at most epsilon under the distribution mu and qprt_{1/8}(g) is the query partition bound of the function g.
Partition bounds were introduced (in both communication complexity and query complexity models) to provide LP-based lower bounds for randomized communication complexity and randomized query complexity. Our results demonstrate that these lower bounds are polynomially tight for product distributions.

Prahladh Harsha, Rahul Jain, and Jaikumar Radhakrishnan. Partition Bound Is Quadratically Tight for Product Distributions. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 135:1-135:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{harsha_et_al:LIPIcs.ICALP.2016.135, author = {Harsha, Prahladh and Jain, Rahul and Radhakrishnan, Jaikumar}, title = {{Partition Bound Is Quadratically Tight for Product Distributions}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {135:1--135:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.135}, URN = {urn:nbn:de:0030-drops-62708}, doi = {10.4230/LIPIcs.ICALP.2016.135}, annote = {Keywords: partition bound, product distribution, communication complexity, query complexity} }

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**Published in:** LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

Suppose Alice holds a uniformly random string X in {0,1}^N and Bob holds a noisy version Y of X where each bit of X is flipped independently with probability epsilon in [0,1/2]. Alice and Bob would like to extract a common random string of min-entropy at least k. In this work, we establish the communication versus success probability trade-off for this problem by giving a protocol and a matching lower bound (under the restriction that the string to be agreed upon is determined by Alice's input X). Specifically, we prove that in order for Alice and Bob to agree on a common string with probability 2^{-gamma k} (gamma k >= 1), the optimal communication (up to o(k) terms, and achievable for large N) is precisely (C *(1-gamma) - 2 * sqrt{ C * (1-C) gamma}) * k, where C := 4 * epsilon * (1-epsilon). In particular, the optimal communication to achieve Omega(1) agreement probability approaches 4 * epsilon * (1-epsilon) * k.
We also consider the case when Y is the output of the binary erasure channel on X, where each bit of Y equals the corresponding bit of X with probability 1-epsilon and is otherwise erased (that is, replaced by a "?"). In this case, the communication required becomes (epsilon * (1-gamma) - 2 * sqrt{ epsilon * (1-epsilon) * gamma}) * k. In particular, the optimal communication to achieve Omega(1) agreement probability approaches epsilon * k, and with no communication the optimal agreement probability approaches 2^{- (1-sqrt{1-epsilon})/(1+sqrt{1-epsilon}) * k}.
Our protocols are based on covering codes and extend the approach of (Bogdanov and Mossel, 2011) for the zero-communication case. Our lower bounds rely on hypercontractive inequalities. For the model of bit-flips, our argument extends the approach of (Bogdanov and Mossel, 2011) by allowing communication; for the erasure model, to the best of our knowledge the needed hypercontractivity statement was not studied before, and it was established (given our application) by (Nair and Wang 2015). We also obtain information complexity lower bounds for these tasks, and together with our protocol, they shed light on the recently popular "most informative Boolean function" conjecture of Courtade and Kumar.

Venkatesan Guruswami and Jaikumar Radhakrishnan. Tight Bounds for Communication-Assisted Agreement Distillation. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{guruswami_et_al:LIPIcs.CCC.2016.6, author = {Guruswami, Venkatesan and Radhakrishnan, Jaikumar}, title = {{Tight Bounds for Communication-Assisted Agreement Distillation}}, booktitle = {31st Conference on Computational Complexity (CCC 2016)}, pages = {6:1--6:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-008-8}, ISSN = {1868-8969}, year = {2016}, volume = {50}, editor = {Raz, Ran}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.6}, URN = {urn:nbn:de:0030-drops-58450}, doi = {10.4230/LIPIcs.CCC.2016.6}, annote = {Keywords: communication complexity, covering codes, hypercontractivity, information theory, lower bounds, pseudorandomness} }

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Complete Volume

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

LIPIcs, Volume 18, FSTTCS'12, Complete Volume

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Proceedings{dsouza_et_al:LIPIcs.FSTTCS.2012, title = {{LIPIcs, Volume 18, FSTTCS'12, Complete Volume}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2013}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012}, URN = {urn:nbn:de:0030-drops-41121}, doi = {10.4230/LIPIcs.FSTTCS.2012}, annote = {Keywords: Software/Program Verification, Models of Computation, Modes of Computation, Complexity Measures and Classes, Nonnumerical Algorithms and Problems Specifying and Verifying and Reasoning about Programs, Mathematical Logic, Formal Languages} }

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Front Matter

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Frontmatter, Table of Contents, Preface, Conference Organization

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. i-xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{dsouza_et_al:LIPIcs.FSTTCS.2012.i, author = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, title = {{Frontmatter, Table of Contents, Preface, Conference Organization}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {i--xiv}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.i}, URN = {urn:nbn:de:0030-drops-38411}, doi = {10.4230/LIPIcs.FSTTCS.2012.i}, annote = {Keywords: Frontmatter, Table of Contents, Preface, Conference Organization} }

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