Let's Make a Difference!

2009/11/05 by Joerg Endrullis, Endrullis, Joerg, Dimitri Hendriks +3 · 1 citation
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Mathematical Dynamics and Fractals #cs.DM #cs.LO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0911.1004

arxiv created 2009/11/05 · openalex publication_date 2009/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behaviour of iterations of the difference operator delta on streams over 0,1. In particular, we show that a stream sigma is eventually periodic if and only if the sequence of differences sigma, delta(sigma), delta(delta(sigma)), ..., the `delta-orbit' of sigma as we call it, is eventually periodic. Moreover, we generalise this result to operations delta_d that sum modulo 2 the elements of each consecutive block of length d+1 in a given 01-stream. Some experimentation with delta-orbits of well-known streams reveals a surprising connexion between the Sierpinski stream and the Mephisto Waltz.

Citations

• Data-Oblivious Stream Productivity

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