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xorshammer.com | ||
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daniellefong.com
The following occurred to me on a run about two years ago: It's not given much press, but the the Halting Problem is intimately related to Gödel's First Incompleteness Theorem. Indeed it produces it as a correllary. Historically, Gödel's incompleteness results were proved by hacking arithmetic into a Turing complete system, and this is still... |
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jeremykun.wordpress.com
We assume the reader is familiar with the concepts of determinism and finite automata, or has read the corresponding primer on this blog. The Mother of All Computers Last time we saw some models for computation, and saw in turn how limited they were. Now, we open Pandrora's hard drive: Definition: A Turing machineis a... |
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nickdrozd.github.io
The classic Busy Beaver function is defined as the maximum number of steps that an N-state 2-color Turing machine program can run before halting when started on the blank tape. The function is uncomputable, and any sound proof system S can only prove values up to a certain point. That is, there is some number Q such that |
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rjlipton.com
Exponential-time algorithms running on large data Moshe Vardi is perhaps the world's foremost expert on the application of logic to practical computations. His paper "Reasoning about Infinite Computations" with Pierre Wolper won the 2000 Gödel Prize. Infinite computations may not seem practical, but the magic is in the finite machines that perform them, and how... |
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