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Separating Words by Automata

Gödel's Lost Letter and P=NP

Jeffrey Shallit is a famous researcher into many things, including number theory and being a skeptic. He has a colorful website with an extensive quotation page—one of my favorites by Howard Aiken is right at the top:

Don’t worry about people stealing an idea. If it’s original, you will have to ram it down their throats.

Today I thought I would discuss a wonderful problem that Jeffrey has worked on.

Jeffrey’s paper is joint with Erik Demaine, Sarah Eisenstat, and David Wilson. See also his talk. They say in their introduction:

Imagine a computing device with very limited powers. What is the simplest computational problem you could ask it to solve? It is not the addition of two numbers, nor sorting, nor string matching—it is telling two inputs apart: distinguishing them in some way.

More formally:

Let $latex {x}&fg=000000&bg=e8e8e8$ and $latex {y}&fg=000000&bg=e8e8e8$ be two distinct $latex {n}&fg=000000&bg=e8e8e8$ long…

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