Results 131 to 140 of about 167 (167)
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The Mathematics Teacher, 1926
We have all heard of pupils who “got by” in geometry by merely memorizing the proofs given in the book and of teachers who permitted them to “get by.” To such persons those proofs were not proofs. Assuming that such methods are passe if they have not passed all together, what limits are we to approach in the other direction?
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We have all heard of pupils who “got by” in geometry by merely memorizing the proofs given in the book and of teachers who permitted them to “get by.” To such persons those proofs were not proofs. Assuming that such methods are passe if they have not passed all together, what limits are we to approach in the other direction?
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Adapting proof automation to adapt proofs
Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018, 2018We extend proof automation in an interactive theorem prover to analyze changes in specifications and proofs. Our approach leverages the history of changes to specifications and proofs to search for a patch that can be applied to other specifications and proofs that need to change in analogous ways.
Talia Ringer +3 more
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1998
To prove that the top-down algorithm in Figure 3.27 terminates, we argue that there is only a finite number of revisables and subsequently only a finite number of possible nodes. With a node being marked in each step of loop (2) the algorithm terminates. The second part of the theorem that H(n) is a hitting-set iff n is a leaf marked ✓ is true since we
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To prove that the top-down algorithm in Figure 3.27 terminates, we argue that there is only a finite number of revisables and subsequently only a finite number of possible nodes. With a node being marked in each step of loop (2) the algorithm terminates. The second part of the theorem that H(n) is a hitting-set iff n is a leaf marked ✓ is true since we
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Proof of Bid as Alternative to Proof of Work
2020Proof of Work (PoW) protocol for cryptocurrency uses an excessive amount of electricity to secure the network. Many PoW coins do not have sufficient hashing power to secure itself. There are many alternatives to PoW, such as Proof of Stake (PoS), merge-mining etcetera, which uses much less electricity.
Wai Kok Chan, Ji-Jian Chin, Vik Tor Goh
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Validation of HOL Proofs by Proof Checking
Formal Methods in System Design, 1999Formal proofs generated by mechanised theorem proving systems may consist of a large number of inferences. As these theorem proving systems are usually very complex, it is extremely difficult if not impossible to formally verify them. This calls for an independent means of ensuring the consistency of mechanically generated proofs.
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Combinatorial proofs and algebraic proofs — II
Resonance, 2013In Part I of this article we considered some binomial identities and also some identities involving the Fibonacci numbers, and proved them using methods which we described as ‘largely’ combinatorial. Now we shift our focus to number theory and to prime numbers in particular, and showcase some proofs having a strong combinatorial element.
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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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Absence of Proof Is Not Proof of Absence
Regional Anesthesia and Pain Medicine, 2011Kenneth C, Cummings, Edward J, Mascha
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