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On the Existence of Algebraically Natural Proofs [article]

Prerona Chatterjee, Mrinal Kumar, C. Ramya, Ramprasad Saptharishi, Anamay Tengse
2021 arXiv   pre-print
on the coefficient vector of h_n.  ...  Our proofs are elementary and rely on the existence of (non-explicit) hitting sets for VP (and VNP) to show that there are efficiently constructible, low degree equations for these classes.  ...  Mrinal thanks Rahul Santhanam and Ben Lee Volk for many insightful conversations about algebraic natural proofs and succinct hitting sets.  ... 
arXiv:2004.14147v2 fatcat:4ikspq4ebjeuxnscucjccfx4by

The Proof of Goldbach's Conjecture on Prime Numbers

Silviu Guiasu
2019 Natural Science  
This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach's Conjecture  ...  Goldbach's Conjecture ("Every even positive integer strictly larger than 4 is the sum of two primes") has remained unproven since 1742.  ...  ACKNOWLEDGEMENTS The author thanks Aveling Mao, Editorial Assistant of Natural Science, for her very valuable advice and suggestions.  ... 
doi:10.4236/ns.2019.119029 fatcat:vs2csase3vdxdnanwebd372z7u

On the nature of the interaction between structures and proof-mass actuators

DAVID C. ZIMMERMAN, DANIEL J. INMAN
1990 Journal of Guidance Control and Dynamics  
GUIDANCE VOL. 13, NO. 1 On the Nature of the Interaction Between Structures and Proof-Mass Actuators David C. Zimmerman* University of Florida, Gainesville, Florida and Daniel J.  ...  The closed-loop system consists of the open-loop system with the proof mass added and the control law turned on.  ... 
doi:10.2514/3.20520 fatcat:e3zdjojoifgxpnzs44uivd4aoa

Formal and Natural Proof: A Phenomenological Approach [chapter]

Merlin Carl
2019 Reflections on the Foundations of Mathematics  
[Rav]) that the formalization of a mathematical proof requires a quality of understanding that subsumes all necessary acts for checking the proof and that, consequently, automatic proof checking cannot  ...  lead to an epistemic gain about a proof.  ...  The mistake becomes obvious when one focuses on the dependencies between the occuring quantities: The δ shown to exist in line 3 of the proof depends on ε, x and n.  ... 
doi:10.1007/978-3-030-15655-8_14 fatcat:yly7zaldzrfj3a7bulqdrvjtdm

Natural proofs versus derandomization

Ryan Williams
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
Strong circuit lower bounds that are "naturalizing" would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing.  ...  We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as NEXP ⊂ TC 0 , which are still wide open.  ...  ). 4 One can make a heuristic argument that the recent proof of NEXP ⊂ ACC ( [Wil11] ) evades Natural Proofs by being non-constructive.  ... 
doi:10.1145/2488608.2488612 dblp:conf/stoc/Williams13 fatcat:ecvxel2o2vdw3aafixugvf4xzu

On an Optical Proof of the Existence of Suspended Matter in Flames1

G. G. STOKES
1891 Nature  
doi:10.1038/045133a0 fatcat:qnhbrzjx2rfzfl3uii36aheqta

Correction to: Formal and Natural Proof: A Phenomenological Approach [chapter]

Merlin Carl
2019 Reflections on the Foundations of Mathematics  
The abstract of this chapter was initially published with error. The chapter has been updated with the corrected abstract as given below.  ...  The updated version of this chapter can be found at https://doi.org/10.1007/978-3-030-15655-8_14  ...  Rav, A critique of a formalist-mechanist version of the justification of arguments in mathematicians' proof practices.  ... 
doi:10.1007/978-3-030-15655-8_22 fatcat:cldejz6ambemlabvejbdmjn2o4

An Evaluation of "The Nature of Proof" Based on the Findings of Raearch on Metacognition
D214 メタ認知研究からみた"The Nature of Proof"の意義と限界

Yoshinori SHIMIZU
1995 Proceedings of the Annual Meeting of Japan Society for Science  
H 本科学教育学会 年会論文集19 ( 1995 ) D214 メ タ 認 知 研 究 か らみ た 「 ' The Naaure of Proof " の 意義 と 限 界 An Evai " atiort of ' " 7he Naaere ' ofPr ' oof ' f Based on the Findings of Researck on Me. tacognition 溝 水 美 憲  ...  ie NatVfe of Proof 「 ( Fawcett , 1938 ) の 実 験 的 な 論 誑 指 導 の コ ー ス に お け る 目標 ・ 手続 き 。 評 価 を 、 メ タ 認 知 研 究 の 成 果 を踏 まえ た 今 日 的 立 場 か ら評 価 し た 。  ... 
doi:10.14935/jssep.19.0_75 fatcat:bctv4uzwkvf5lnwm6avk2erlaq

Foundations for natural proofs and quantifier instantiation

Christof Löding, P. Madhusudan, Lucas Peña
2017 Proceedings of the ACM on Programming Languages  
explains the efficacy of verification engines like natural proofs that resort to such heuristics.  ...  We give foundational results that explain the efficacy of heuristics used for dealing with quantified formulas and recursive definitions.  ...  We would also like to thank Mahesh Viswanathan and Xiaokang Qiu for early discussions on automatic discovery of induction principles for natural proofs.  ... 
doi:10.1145/3158098 dblp:journals/pacmpl/LodingMP18 fatcat:u5xnpsg2arbuxovuyvwmkdddoa

Determining Semantic Textual Similarity using Natural Deduction Proofs

Hitomi Yanaka, Koji Mineshima, Pascual Martínez-Gómez, Daisuke Bekki
2017 Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing  
natural deduction proofs.  ...  For the natural deduction proofs, we use ccg2lambda, a higherorder automatic inference system, which converts Combinatory Categorial Grammar (CCG) derivation trees into semantic representations and conducts  ...  Acknowledgments We thank the three anonymous reviewers for their detailed comments. This work was supported by JST CREST Grant Number JPMJCR1301, Japan.  ... 
doi:10.18653/v1/d17-1071 dblp:conf/emnlp/YanakaMMB17 fatcat:dq5kuwlnonasdpu6nmzuoorcwy

An Assertional Proof of the Stability and Correctness of Natural Mergesort

K. Rustan M. Leino, Paqui Lucio
2015 ACM Transactions on Computational Logic  
Along the paper we provide -and explain-the complete text of the program-proof.  ...  We present a mechanically verified implementation of the sorting algorithm commonly known as Natural Mergesort.  ...  Acknoledgments We are very grateful to Jean-Christophe Filliâtre for many valuable comments on a previous draft of this paper.  ... 
doi:10.1145/2814571 fatcat:wriehlpxhvahhju3zcypnduoma

Natural proof of the characterization of relatively compact families in L^p-spaces on locally compact groups [article]

Mateusz Krukowski
2020 arXiv   pre-print
At first glance, the suggested approach may seem convoluted and lengthy, but we spare no effort to argue that our proof is in fact more natural than the ones existent in the literature.  ...  In the paper we look for an elegant proof of the characterization of relatively compact families in L^p-spaces.  ...  I also wish to thank Robert Stańczy for the reference to the Arzelà-Ascoli theorem for C 0 (X) in the monograph "Integral Equations and Stability of Feedback Systems" by Constantin Corduneanu.  ... 
arXiv:1801.01898v3 fatcat:eyomkyfjfjh2haysoaha365tue

The Circuit-Input Game, Natural Proofs, and Testing Circuits With Data

Brynmor Chapman, Ryan Williams
2015 Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15  
We show how the Natural Proofs barrier may be potentially sidestepped, by simply focusing on analyzing circuits that check their answers.  ...  (Note, via self-reducibility, any small circuit can be turned into one of this kind!) The proof is very general; similar equivalences hold for other lower bound problems.  ...  Acknowledgements We thank the ITCS reviewers for their helpful comments. In particular, one reviewer improved an earlier version of Theorem 2.3.  ... 
doi:10.1145/2688073.2688115 dblp:conf/innovations/ChapmanW15 fatcat:dxgjg4xysnebvjhabo7uss6caa

Natural proofs for structure, data, and separation

Xiaokang Qiu, Pranav Garg, Andrei Ştefănescu, Parthasarathy Madhusudan
2013 Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13  
We propose natural proofs for reasoning with programs that manipulate data-structures against specifications that describe the structure of the heap, the data stored within it, and separation and framing  ...  We develop ways to reason with heaplets using classical logic over the theory of sets, and develop natural proofs for reasoning using proof tactics involving disciplined unfoldings and formula abstractions  ...  The natural proof methodology: Our proof methodology of natural proofs was first proposed in a paper by Madhusudan et al on natural proofs for tree data-structures last year at POPL [27] .  ... 
doi:10.1145/2491956.2462169 dblp:conf/pldi/Qiu0SM13 fatcat:wjy3m744nnglvpdah23fhbckn4

The Standpoint of Bhāviveka and Kamalaśīla in Proving Absence of Self-nature: Focusing on the Proof of Being not from no Cause

Genkai Hayashi
2018 JOURNAL OF INDIAN AND BUDDHIST STUDIES (INDOGAKU BUKKYOGAKU KENKYU)  
PrasP Prasannapadā of Candrakīrti. In Clear Words: The Prasannapadā, Chapter One. Vol. I, Introduction, Manuscript Description, Sanskrit Texts. Ed. Macdonald Anne.  ...  Vienna: Austrian Academy of Sciences, 2015. SDNS Sarvadharmaniḥsvabhāvasiddhi of Kamalaśīla. See 1982 TA Tattvāloka of Kamalaśīla, D 3888 sa 244b1-273a4, P 101 5288 sa 275a4-312a5.  ... 
doi:10.4259/ibk.67.1_390 fatcat:gvzrklmfpvbzbirlusyxkkpd2e
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