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Electronic Colloquium on Computational Complexity

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TR21-113 | 25th July 2021
Nikhil Mande, Ronald de Wolf

Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting the optimal constant factors in the leading terms in a number of different models.

The following are our results in the randomized model:

1) We give a general technique to convert ... more >>>


TR21-112 | 30th July 2021
Vikraman Arvind, Venkatesan Guruswami

CNF Satisfiability in a Subspace and Related Problems

We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the Union-of-Subspace Avoidance (USA) problem), and finding a common zero of a system of ... more >>>


TR21-111 | 19th July 2021
Aniruddha Biswas, Palash Sarkar

Influence of a Set of Variables on a Boolean Function

Revisions: 2

The influence of a set of variables on a Boolean function has three separate definitions in the literature, the first due to Ben-Or and Linial (1989), the second due to Fischer et al. (2002) and Blais (2009) and the third due to Tal (2017). The goal of the present work ... more >>>



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