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Electronic Colloquium on Computational Complexity

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TR20-022 | 19th February 2020
Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Interactive Error Resilience Beyond $\frac{2}{7}$

Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against?

For the non-adaptive channel, where the parties must agree ... more >>>

TR20-021 | 21st February 2020
Rahul Ilango, Bruno Loff, Igor Carboni Oliveira

NP-Hardness of Circuit Minimization for Multi-Output Functions

Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of Cook and Levin in the early 1970s, a central question is whether minimizing the circuit size of an ... more >>>

TR20-020 | 21st February 2020
Nikhil Mande, Justin Thaler, Shuchen Zhu

Improved Approximate Degree Bounds For $k$-distinctness

An open problem that is widely regarded as one of the most important in quantum query complexity is to resolve the quantum query complexity of the $k$-distinctness function on inputs of size $N$. While the case of $k=2$ (also called Element Distinctness) is well-understood, there is a polynomial gap between ... more >>>

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