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Different techniques have been used to prove several transference theorems of the form " non-trivial algorithms for a circuit class C yield circuit lower bounds against C ". In this survey we revisit many of these results. We discuss how circuit lower bounds can be obtained from deran-domization, compression, learning, and satisfiability algorithms. We also… (More)

The graph reconstruction conjecture asserts that a finite simple graph on at least 3 vertices can be reconstructed up to isomorphism from its deck-the collection of its vertex-deleted subgraphs. Kocay's Lemma is an important tool in graph reconstruction. Roughly speaking, given the deck of a graph G and any finite sequence of graphs, it gives a linear… (More)

We establish unconditionally that for every integer k ≥ 1 there is a language L ∈ P such that it is consistent with Cook's theory PV that L / ∈ SIZE(n k). Our argument is non-constructive and does not provide an explicit description of this language.

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