3 ms·
Semi-Thue System
- dfischer 6y agoIt’s on my list to get more comfortable with fundamental concepts rooted in hashing, cryptography, and general abstract computational theories. Intuitively this seems relevant based on a potentially infinite square free set and applying it to those concepts. What unique things can you do when you have an infinite series of unique combinations that are computable with lower and upper bounds and into buckets? Seems like lots of interesting possibilities to compression and computation. Maybe I’m overthinking it but this seems super interesting to understand more. Perhaps if anyone can help thread the needle between the theoretical implications to any real world examples? Thanks! Edit: makes me think of ternary logic computers or potentially 4 valued and isomorphic properties to quantum computing. The article linked coincidentally mentions a quantum thue computer. Edit 2: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.65.970&rep=rep1&type=pdf https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.65...
- dfischer 6y agoFound some decently approachable text here: http://ion.uwinnipeg.ca/~nrampers/rampersad_thesis.pdf http://ion.uwinnipeg.ca/~nrampers/rampersad_thesis.pdf And one more: https://arxiv.org/pdf/2001.11763.pdf https://arxiv.org/pdf/2001.11763.pdf
- dfischer 6y agoAlso interestingly related: to Gould's sequence, Pascal's Triangle and Sierpinski (why?): https://en.wikipedia.org/wiki/Gould%27s_sequence#cite_note-5 https://en.wikipedia.org/wiki/Gould%27s_sequence#cite_note-5 Some element of 3 dependent on fractal, l-expressions? Similar to cantor set? More: https://en.wikipedia.org/wiki/Sharkovskii%27s_theorem https://en.wikipedia.org/wiki/Sharkovskii%27s_theorem More 2: https://en.wikipedia.org/wiki/Period_three_implies_chaos https://en.wikipedia.org/wiki/Period_three_implies_chaos Why is 3 so special? Hmm...