Results 211 to 220 of about 2,128,058 (249)
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ON SKOLEMIZATION AND PROOF COMPLEXITY
Fundamenta Informaticae, 1994The impact of Skolemization on the complexity of proofs in the sequent calculus is investigated. It is shown that prefix Skolemization may result in a nonelementary increase of Herbrand complexity (i. e. the minimal number of constituents in a Herbrand disjunction) versus structural Skolemization.
Matthias Baaz, Alexander Leitsch
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Journal of Symbolic Logic, 1981
In a recent article in this Journal (see [3]), J.P. Jones states and proves a theorem which purports to give an “absolute epistemological upper bound on the complexity of mathematical proofs” for recursively axiomatizable theories. However, Jones' statement of this result is misleading, and in fact defective, as can be seen by a close analysis of it ...
William S. Hatcher, Bernard R. Hodgson
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In a recent article in this Journal (see [3]), J.P. Jones states and proves a theorem which purports to give an “absolute epistemological upper bound on the complexity of mathematical proofs” for recursively axiomatizable theories. However, Jones' statement of this result is misleading, and in fact defective, as can be seen by a close analysis of it ...
William S. Hatcher, Bernard R. Hodgson
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Proof Complexity and Textual Cohesion
Journal of Logic, Language and Information, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eli Dresner
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The Complexity of Propositional Proofs
Bulletin of Symbolic Logic, 1995§1. Introduction. The classical propositional calculus has an undeserved reputation among logicians as being essentially trivial. I hope to convince the reader
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2009
This note exposes few basic points of proof complexity in a way accessible to any ...
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This note exposes few basic points of proof complexity in a way accessible to any ...
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Journal of Logic and Computation, 2005
Summary: We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are \(\Pi_1^0\)-hard and obviously ...
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Summary: We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are \(\Pi_1^0\)-hard and obviously ...
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On Proof Complexity of Circumscription
1998Circumscription is a non-monotonic formalism based on the idea that objects satisfying a certain predicate expression are considered as the only objects satisfying it. Theoretical complexity results imply that circumscription is (in the worst case) computationally harder than classical logic.
Uwe Egly, Hans Tompits
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Highly complex proofs and implications of such proofs
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005Abstract Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as mathematics continues to mature, more examples are likely to appear. Such proofs raise various issues.
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The Proof Complexity of Polynomial Identities
2009 24th Annual IEEE Conference on Computational Complexity, 2009Devising an efficient deterministic -- or even a non-deterministic sub-exponential time -- algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of _proving_ polynomial identities. To this
Pavel Hrubes, Iddo Tzameret
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On Regular Expression Proof Complexity
2017We investigate the proof complexity of Salomaa’s axiom system \(F_1\) for regular expression equivalence. We show that for two regular expression E and F over the alphabet \(\varSigma \) with \(L(E)=L(F)\) an equivalence proof of length \(O\left( |\varSigma |^4\cdot \textsc {Tower}(\max \{h(E),h(F)\}+4)\right) \) can be derived within \(F_1\), where h ...
Simon Beier, Markus Holzer 0001
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