Results 231 to 240 of about 1,041,680 (279)
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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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ACM SIGLOG News, 2016
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to old problems, and new directions of research. In particular, we focus on tight connections between proof complexity
Toniann Pitassi, Iddo Tzameret
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We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to old problems, and new directions of research. In particular, we focus on tight connections between proof complexity
Toniann Pitassi, Iddo Tzameret
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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.
Baaz, Matthias, Leitsch, Alexander
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Highly complex proofs and implications of such proofs
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005Conventional 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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2002
A weak formal theory of arithmetic is developed, entirely analogous to classical arithmetic but with two separate kinds of variables: induction variables and quantifier variables. The point is that the provably recursive functions are now more feasibly computable than in the classical case, lying between Grzegorczyk’s E2 and E3, and their computational
G. E. Ostrin, S. S. Wainer
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A weak formal theory of arithmetic is developed, entirely analogous to classical arithmetic but with two separate kinds of variables: induction variables and quantifier variables. The point is that the provably recursive functions are now more feasibly computable than in the classical case, lying between Grzegorczyk’s E2 and E3, and their computational
G. E. Ostrin, S. S. Wainer
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Oberwolfach Reports, 2018
Proof complexity is a multi-disciplinary intellectual endeavor that addresses questions of the general form “how difficult is it to prove certain mathematical facts?” The current workshop focused on recent advances in our understanding of logic-based proof systems and on connections to algorithms, geometry and combinatorics research, such as the ...
Albert Atserias +3 more
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Proof complexity is a multi-disciplinary intellectual endeavor that addresses questions of the general form “how difficult is it to prove certain mathematical facts?” The current workshop focused on recent advances in our understanding of logic-based proof systems and on connections to algorithms, geometry and combinatorics research, such as the ...
Albert Atserias +3 more
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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.
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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 ...
Hatcher, William S., Hodgson, Bernard R.
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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 ...
Hatcher, William S., Hodgson, Bernard R.
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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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