All reports by Author James Cook:

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TR20-056
| 17th April 2020
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James Cook, Ian Mertz#### Catalytic Approaches to the Tree Evaluation Problem

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TR12-175
| 13th December 2012
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James Cook, Omid Etesami, Rachel Miller, Luca Trevisan#### On the One-Way Function Candidate Proposed by Goldreich

Revisions: 1

James Cook, Ian Mertz

The study of branching programs for the Tree Evaluation Problem, introduced by S. Cook et al. (TOCT 2012), remains one of the most promising approaches to separating L from P. Given a label in $[k]$ at each leaf of a complete binary tree and an explicit function in $[k]^2 \to ... more >>>

James Cook, Omid Etesami, Rachel Miller, Luca Trevisan

A function $f$ mapping $n$-bit strings to $m$-bit strings can be constructed from a bipartite graph with $n$ vertices on the left and $m$ vertices on the right having right-degree $d$ together with a predicate $P:\{0,1\}^d\rightarrow\{0,1\}$. The vertices on the left correspond to the bits of the input to the ... more >>>