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TR23-189
| 28th November 2023
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John Kallaugher, Ojas Parekh, Nadezhda Voronova#### Exponential Quantum Space Advantage for Approximating Maximum Directed Cut in the Streaming Model

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TR23-188
| 28th November 2023
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Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu#### Parameterized Inapproximability Hypothesis under ETH

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TR23-187
| 27th November 2023
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Klim Efremenko, Michal Garlik, Dmitry Itsykson#### Lower bounds for regular resolution over parities

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John Kallaugher, Ojas Parekh, Nadezhda Voronova

While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in which elements arrive and must be processed sequentially without random access, but these have been ... more >>>

Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu

The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to satisfy an $\varepsilon$ fraction of constraints for some absolute constant $\varepsilon > 0$. PIH plays the role of ... more >>>

Klim Efremenko, Michal Garlik, Dmitry Itsykson

The proof system resolution over parities (Res($\oplus$)) operates with disjunctions of linear equations (linear clauses) over $\mathbb{F}_2$; it extends the resolution proof system by incorporating linear algebra over $\mathbb{F}_2$. Over the years, several exponential lower bounds on the size of tree-like Res($\oplus$) refutations have been established. However, proving a superpolynomial ... more >>>

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