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Electronic Colloquium on Computational Complexity

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Reports tagged with Equality:
TR08-085 | 19th June 2008
Farid Ablayev, Airat Khasianov, Alexander Vasiliev

On Complexity of Quantum Branching Programs Computing Equality-like Boolean Functions

Revisions: 1

We consider Generalized Equality, the Hidden Subgroup,
and related problems in the context of quantum Ordered Binary
Decision Diagrams. For the decision versions of considered problems
we show polynomial upper bounds in terms of quantum OBDD width. We
apply a new modification of the fingerprinting technique and present
the algorithms ... more >>>

TR11-152 | 12th November 2011
Emanuele Viola

The communication complexity of addition

Suppose each of $k \le n^{o(1)}$ players holds an $n$-bit number $x_i$ in its hand. The players wish to determine if $\sum_{i \le k} x_i = s$. We give a public-coin protocol with error $1\%$ and communication $O(k \lg k)$. The communication bound is independent of $n$, and for $k ... more >>>

TR12-153 | 9th November 2012
Joshua Brody, Amit Chakrabarti, Ranganath Kondapally

Certifying Equality With Limited Interaction

Revisions: 1

The \textsc{equality} problem is usually one's first encounter with
communication complexity and is one of the most fundamental problems in the
field. Although its deterministic and randomized communication complexity
were settled decades ago, we find several new things to say about the
problem by focusing on two subtle aspects. The ... more >>>

TR16-111 | 20th July 2016
Amit Chakrabarti, Sagar Kale

Strong Fooling Sets for Multi-Player Communication with Applications to Deterministic Estimation of Stream Statistics

We develop a paradigm for studying multi-player deterministic communication,
based on a novel combinatorial concept that we call a {\em strong fooling
set}. Our paradigm leads to optimal lower bounds on the per-player
communication required for solving multi-player $\textsc{equality}$
problems in a private-message setting. This in turn gives a ... more >>>

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