Soren Riis, Meera Sitharam

The semantics of decision problems are always essentially independent of the

underlying representation. Thus the space of input data (under appropriate

indexing) is closed

under action of the symmetrical group $S_n$ (for a specific data-size)

and the input-output relation is closed under the action of $S_n$.

more >>>

Alexander Razborov, Sergey Yekhanin

A two server private information retrieval (PIR) scheme

allows a user U to retrieve the i-th bit of an

n-bit string x replicated between two servers while each

server individually learns no information about i. The main

parameter of interest in a PIR scheme is its communication

complexity, namely the ...
more >>>

Manuel Arora, GĂˇbor Ivanyos, Marek Karpinski, Nitin Saxena

The problem of finding a nontrivial factor of a polynomial $f(x)$ over a finite field $\mathbb{F}_q$ has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the ... more >>>

Joshua Grochow

Mahaney's Theorem states that, assuming P $\neq$ NP, no NP-hard set can have a polynomially bounded number of yes-instances at each input length. We give an exposition of a very simple unpublished proof of Manindra Agrawal whose ideas appear in Agrawal-Arvind ("Geometric sets of low information content," Theoret. Comp. Sci., ... more >>>

Daniel Kane, Shachar Lovett, Sankeerth Rao

Assume that the edges of the complete bipartite graph $K_{n,n}$ are labeled with elements of $\mathbb{F}_2^d$, such that the sum over

any simple cycle is nonzero. What is the smallest possible value of $d$? This problem was raised by Gopalan et al. [SODA 2017] as it characterizes the alphabet size ...
more >>>

Joshua Grochow, Cris Moore

In 1969, Strassen shocked the world by showing that two n x n matrices could be multiplied in time asymptotically less than $O(n^3)$. While the recursive construction in his algorithm is very clear, the key gain was made by showing that 2 x 2 matrix multiplication could be performed with ... more >>>

Ankit Garg, Visu Makam, Rafael Mendes de Oliveira, Avi Wigderson

We consider the problem of outputting succinct encodings of lists of generators for invariant rings. Mulmuley conjectured that there are always polynomial sized such encodings for all invariant rings. We provide simple examples that disprove this conjecture (under standard complexity assumptions).

more >>>