Games Between Programs: The Ruliology of Competition(writings.stephenwolfram.com)

writings.stephenwolfram.com

Games Between Programs: The Ruliology of Competition

https://writings.stephenwolfram.com/2026/06/games-between-programs-the-ruliology-of-competition/

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In the middle of this too-long-and-rambling piece, there's a sketch of an interesting sequence: look for the text "universal winner." Let a(n) be the size of the smallest "coin-matching player" DFA that eventually matches the output of its n-state opponent no matter the identity of that opponent. a(1) is obviously 2 (right?); Wolfram indicates a(2) <= 10; what is a(3)?

This is different from the problem of identifying the opponent, which obviously requires at least as many states as there are opponents.

Is this sequence in the OEIS? Is a(3) even known?

ac50hz先月

Looks like it’s time for me to revisit my 1st edition of a New Kind of Science, for a refresher.