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ECCC
Electronic Colloquium on Computational Complexity

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REPORTS > 2025:
All reports in year 2025:
TR25-014 | 18th February 2025
Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, Raghuvansh Saxena

Information Dissemination via Broadcasts in the Presence of Adversarial Noise

We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where $n$ parties, each holding an input bit, wish to know each other's input. For this, they communicate in rounds, where, in each round, one designated party sends ... more >>>


TR25-013 | 18th February 2025
Raghuvansh Saxena, Yael Tauman Kalai

Polynomial Size, Short-Circuit Resilient Circuits for NC

We show how to convert any circuit of poly-logarithmic depth and polynomial size into a functionally equivalent circuit of polynomial size (and polynomial depth) that is resilient to adversarial short-circuit errors. Specifically, the resulting circuit computes the same function even if up to $\epsilon d$ gates on every root-to-leaf path ... more >>>


TR25-012 | 17th February 2025
Dean Doron, Ori Fridman

Bit-Fixing Extractors for Almost-Logarithmic Entropy

An oblivious bit-fixing source is a distribution over $\{0,1\}^n$, where $k$ bits are uniform and independent and the rest $n-k$ are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity ... more >>>


TR25-011 | 17th February 2025
Oded Goldreich, Roei Tell

Complexity theoretic implications of pseudodeterministic algorithms for PPT-search problems

Pseudodeterministic algorithms are probabilistic algorithms that solve search problems but do so by always providing the same (``canonical'') solution to a given instance, except with small probability.
While the complexity theoretic implications of pseudodeterministic algorithms were explored in the past, we suggest to conduct this exploration within the framework ... more >>>


TR25-010 | 11th February 2025
Marshall Ball, Lijie Chen, Roei Tell

Towards Free Lunch Derandomization from Necessary Assumptions (and OWFs)

The question of optimal derandomization, introduced by Doron et. al (JACM 2022), garnered significant recent attention. Works in recent years showed conditional superfast derandomization algorithms, as well as conditional impossibility results, and barriers for obtaining superfast derandomization using certain black-box techniques.

Of particular interest is the extreme high-end, which ... more >>>


TR25-009 | 7th February 2025
Marco Aldi, Sevag Gharibian, Dorian Rudolph

An unholy trinity: TFNP, polynomial systems, and the quantum satisfiability problem

The theory of Total Function NP (TFNP) and its subclasses says that, even if one is promised an efficiently verifiable proof exists for a problem, finding this proof can be intractable. Despite the success of the theory at showing intractability of problems such as computing Brouwer fixed points and Nash ... more >>>


TR25-008 | 9th February 2025
Shubhangi Saraf, Devansh Shringi

Reconstruction of Depth $3$ Arithmetic Circuits with Top Fan-in $3$

In this paper, we give the first subexponential (and in fact quasi-polynomial time) reconstruction algorithm for depth 3 circuits of top fan-in 3 ($\Sigma\Pi\Sigma(3)$ circuits) over the fields $\mathbb{R}$ and $\mathbb C$. Concretely, we show that given blackbox access to an $n$-variate polynomial $f$ computed by a $\Sigma\Pi\Sigma(3)$ circuit of ... more >>>


TR25-007 | 5th February 2025
Amir Shpilka

Improved Debordering of Waring Rank

We prove that if a degree-$d$ homogeneous polynomial $f$ has border Waring rank $\underline{\mathrm{WR}}({f}) = r$, then its Waring rank is bounded by
\[
{\mathrm{WR}}({f}) \leq d \cdot r^{O(\sqrt{r})}.
\]
This result significantly improves upon the recent bound ${\mathrm{WR}}({f}) \leq d \cdot 4^r$ established in [Dutta, Gesmundo, Ikenmeyer, Jindal, ... more >>>


TR25-006 | 4th February 2025
Subhash Khot, Kunal Mittal

Biased Linearity Testing in the 1% Regime

We study linearity testing over the $p$-biased hypercube $(\{0,1\}^n, \mu_p^{\otimes n})$ in the 1% regime. For a distribution $\nu$ supported over $\{x\in \{0,1\}^k:\sum_{i=1}^k x_i=0 \text{ (mod 2)} \}$, with marginal distribution $\mu_p$ in each coordinate, the corresponding $k$-query linearity test $\text{Lin}(\nu)$ proceeds as follows: Given query access to a function ... more >>>


TR25-005 | 31st January 2025
Joshua Brakensiek, Venkatesan Guruswami, Sai Sandeep

SDPs and Robust Satisfiability of Promise CSP

For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust satisfaction algorithms are precisely those of bounded width, i.e., CSPs whose satisfiability can be ... more >>>


TR25-004 | 17th January 2025
Songhua He

A note on a hierarchy theorem for promise-BPTIME

We prove a time hierarchy theorem for the promise-BPTIME. This is considered to be a folklore problem and was thought to follow from the existence of complete problems or through direct diagonalization. We observe that neither argument carries through in some immediate way in the promise version. However, the hierarchy ... more >>>


TR25-003 | 16th January 2025
William Hoza

Fooling Near-Maximal Decision Trees

For any constant $\alpha > 0$, we construct an explicit pseudorandom generator (PRG) that fools $n$-variate decision trees of size $m$ with error $\epsilon$ and seed length $(1 + \alpha) \cdot \log_2 m + O(\log(1/\epsilon) + \log \log n)$. For context, one can achieve seed length $(2 + o(1)) \cdot ... more >>>


TR25-002 | 14th January 2025
Vinayak Kumar

New Pseudorandom Generators and Correlation Bounds Using Extractors

We establish new correlation bounds and pseudorandom generators for a collection of computation models. These models are all natural generalizations of structured low-degree $F_2$-polynomials that we did not have correlation bounds for before. In particular:

1. We construct a PRG for width-2 $poly(n)$-length branching programs which read $d$ bits ... more >>>


TR25-001 | 12th January 2025
Benny Applebaum, Oded Nir

The Meta-Complexity of Secret Sharing

A secret-sharing scheme allows the distribution of a secret $s$ among $n$ parties, such that only certain predefined “authorized” sets of parties can reconstruct the secret, while all other “unauthorized” sets learn nothing about $s$. The collection of authorized/unauthorized sets is defined by a monotone function $f: \{0,1\}^n \rightarrow \{0,1\}$. ... more >>>




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