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accodeing.com
| | rjlipton.com

Another proof idea using finite automata Steve Cook proved three landmark theorems with 1971 dates. The first has been called a "surprising theorem": that any deterministic pushdown automaton with two-way input tape can be simulated in linear time by a random-access machine. This implies that string matching can be done in linear time, which inspired...
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| | nickdrozd.github.io

How long can a Turing machine program run when started on the blank tape before the tape becomes blank again? Of course, this will depend on the length of the program - how many states and colors it has. Even given these parameters, it is logically impossible to calculate how long a self-cleaning Turing machine can run. Any values that can be known have to be discovered empirically.
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| | blog.paulhankin.net

Programming, Computer Science, Games and Other Things
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| | scottaaronson.blog

(Thanks to Amit Sahai for spurring me to write this post!) The Background We all remember Gödel's First Incompleteness Theorem from kindergarten. This is the thing that, given a formal system F, constructs a sentence G(F) that's a mathematical encoding of "This sentence is not provable in F." If F proves G(F), then F proves...
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