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The Complexity of Local Stratification - SUrface
The Complexity of Local Stratification - SUrface

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... (Direct Proof) If n is an odd natural number, then n2 is odd. Proof: An integer n is called odd if it is of the form n = 2k +1 for some integer k , then since we assumed n odd, we can write n = 2k +1. Squaring gives n2 = (2k +1)2 ...
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What is a proof? - Computer Science

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Chapter 17 Proof by Contradiction

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mathematical logic: constructive and non

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Symbol/Membrane Complexity of P Systems with Symport/Antiport

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Turing's proof

Turing's proof is a proof by Alan Turing, first published in January 1937 with the title On Computable Numbers, With an Application to the Entscheidungsproblem. It was the second proof of the assertion (Alonzo Church's proof was first) that some decision problems are ""undecidable"": there is no single algorithm that infallibly gives a correct ""yes"" or ""no"" answer to each instance of the problem. In his own words:""...what I shall prove is quite different from the well-known results of Gödel ... I shall now show that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]..."" (Undecidable p. 145).Turing preceded this proof with two others. The second and third both rely on the first. All rely on his development of type-writer-like ""computing machines"" that obey a simple set of rules and his subsequent development of a ""universal computing machine"".
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