Small circuits and dual weak PHP in the universal theory of p-time algorithms
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We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending n bits to m ≥ n^2 bits violates the dual weak pigeonhole principle: every string y of length m equals to the value of the function for some x of length n. The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size n^d.
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