ChatGPTs rather underwhelming performance on a formal problem
The MIU System was introduced by Douglas R. Hofstadter in his fabulous book Goedel, Escher, Bach . The formal system acts on chains (words) resembled from a three letter alphabet (the set MIU) and four simple rules. If your chain ends with an „I“ you may append a „U“. Example: MI - (1) - MIU If your chain looks like „Mx“ (starts with „M“ followed by an arbitrary sequence of letters) you may write „Mxx“ You can replace „III“ with „U“ You can delete the sequence „UU“ Let me give you just a few examples: MIIIU - (3) - MUU - (4) - M. So from „MIIIU“, there is a series of operations to transform it to „M“. MIU - (2) - MIUIU MUIIIU - (2) - MUIIIUUIIIU - (4) - MUIIIIIIU - (2x3) - MUUUU - (2x4) - M (Hofstadter asks, whether it is possible to transform „MI“ into „MU“ , try it. You will not find a spoiler in this post.) I hope you agree that this sounds like a quite simple system made up of pure logic - something a computer should be good at and so: let’s ask our friendly Chat...