On Kolmogorov Complexity of Random Very Long Braided Words
Dara O Shayda

TL;DR
This paper investigates how Braid group relations significantly reduce the Kolmogorov Complexity of random words, revealing distinct reduction bands and suggesting a universal distribution pattern across algebraic structures.
Contribution
It introduces a novel empirical analysis of Kolmogorov Complexity reduction via Braid relations and proposes the universality of these distribution patterns beyond Braid groups.
Findings
Braid relations cause substantial complexity reduction in random words.
Distinct bands of complexity reduction are observed with gaps in between.
Empirical evidence suggests universality of these reduction distributions.
Abstract
Any positive word comprised of random sequence of tokens form a finite alphabet can be reduced (without change of length) using an appropriate size Braid group relationships. Surprisingly the Braid relations dramatically reduce the Kolmogorov Complexity of the original random word and do so in distinct bands of (rate of change) values with gaps in between. Distribution of these bands are estimated and empirical statistics collected by actually coding approximations to the Kolmogorov Complexity (in Mathematica 9.0). Lempel-Ziv-Welch lossless compression algorithm techniques used to estimate the distribution for gaped bands. Evidence provided that such distributions of reduction in Kolmogorov Complexity based upon Braid groups are universal i.e. they can model more general algebraic structures other than Braid groups.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Algorithms and Data Compression
