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We define constructive truth for arithmetic and for intuitionistic analysis, and investigate its properties. We also prove that the set of constructively true (first order) arithmetical statements is Π 1 2 and Σ 1 2 hard, and we conjecture it to be complete for second order arithmetic. A statement is constructively true iff it is realized by a constructive… (More)
We prove that uniform circuits of size n can be evaluated in space O(n/log n). Thus, Space(O(n)) is not in uniform Size(o(n*log n)). For uniformity, we only require that the circuit is O(n/log n)-Space uniform. We also generalize the construction to prove that a machine with O(n^delta) (delta<1) internal storage and O(2^n^delta) length single-bit-access… (More)