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Metamathematics of First-Order Arithmetic
This chapter discusses Arithmetic as Number Theory, Set Theory and Logic, Fragments and Combinatorics, and Models of Fragments of Arithmetic.
Lower bounds for resolution and cutting plane proofs and monotone computations
- P. Pudlák
- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1 September 1997
An exponential lower bound on the length of cutting plane proofs is proved using an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates.
An improved exponential-time algorithm for k-SAT
- R. Paturi, P. Pudlák, M. Saks, F. Zane
- Computer ScienceProceedings 39th Annual Symposium on Foundations…
- 1 May 2005
It is shown that, for each k, the running time of ResolveSat on a k-CNF formula is significantly better than 2/sup n/, even in the worst case, and the idea of succinctly encoding satisfying solutions can be applied to obtain lower bounds on circuit site.
Satisfiability Coding Lemma
- R. Paturi, P. Pudlák, F. Zane
- Computer ScienceProceedings 38th Annual Symposium on Foundations…
- 19 October 1997
This basic lemma shows how to encode satisfying solutions of a /spl kappa/-CNF succinctly as well as an upper and lower bound on the size of depth 3 circuits of AND and OR gates computing the parity function.
Propositional proof systems, the consistency of first order theories and the complexity of computations
The problem about the length of proofs of the sentences saying that there is no proof of contradiction in S whose length is < n is considered and the relation of this problem to some problems about propositional proof systems is shown.
Bounded Arithmetic and the Polynomial Hierarchy
Cuts, consistency statements and interpretations
- P. Pudlák
- Computer ScienceJournal of Symbolic Logic
- 1 June 1985
This paper wants to study statements for nonreflexive theories, especially for finitely axiomatizable theories (which are never reflexive).
On Reducibility and Symmetry of Disjoint NP-Pairs
- P. Pudlák
Among others, it is proved that the Broken Mosquito Screen pair of disjoint NP sets can be polynomially reduced to Clique–Coloring pair and thus is polynOMially separable and it is shown that the pair ofDisjointNP sets canonically associated with the Resolution proof system is symmetric.
Threshold circuits of bounded depth
Quantified propositional calculi and fragments of bounded arithmetic
It is shown that nontrivial statements about S2 and its fragments can be derived from this relation, in particular: for i > j ~ 2 the V1:J-consequences if S~ are finitely axiomatizable, which would require proving superpolynomial lower bounds to the length of proofs in proof systems G.