J. Johannsen. Equational calculi and constant-depth propositional proofs. In P. Beame and S. Buss, editors, Proof Complexity and Feasible Arithmetics, volume 39. AMS DIMACS Series, 1998. Home/Search Document Details and Download
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On Threshold Logic and Cutting Planes Proofs - Clote, Johannsen (1998) Self-citation (Johannsen) (Correct)
.... : The correctness of PTK is obvious, and the completeness follows from Theorem 1 below and the completeness of PTK. In the following, we show that PTK and PTK are polynomially equivalent, and that the mutual simulations also respect the depth of proofs. This was claimed without proof in [3], where PTK was rst de ned. Theorem 1. If P is a proof in PTK, then there is a proof P 0 in PTK of the same end sequent. The size of P 0 is linear in the size of P , and the formula depths of P and P 0 are the same. Proof. Each application of the rule T n k right is replaced by a ....
J. Johannsen. Equational calculi and constant-depth propositional proofs. In P. Beame and S. R. Buss, editors, Proof Complexity and Feasible Arithmetics, pages 149-162. AMS DIMACS Series Vol. 39, 1998. 8
VTC0: A Second-Order Theory for TC0 - Nguyen, Cook (Correct)
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J. Johannsen. Equational calculi and constant-depth propositional proofs. In P. Beame and S. Buss, editors, Proof Complexity and Feasible Arithmetics, volume 39. AMS DIMACS Series, 1998.
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