2011/01/23 by Nithin Nagaraj, Mathew Shaji Kavalekalam, Nagaraj, Nithin +5 · 1 citation
Computer Science · #Algorithms and Data Compression #Chaotic Dynamics (nlin.CD) #Computability, Logic, AI Algorithms #Cryptography and Security (cs.CR) #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.1101.4341
openalex publication_date 2011/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm first proposed by W. Ebeling et al. [Math. Biosc. 52, 1980] and Jiménez-Montaño et al. [arXiv:cond-mat/0204134, 2002]) which was subsequently shown to be optimal. NSPRS has also been used to estimate Entropy of written English (P. Grassberger [arXiv:physics/0207023, 2002]). We propose a new measure of complexity - defined as the number of iterations of NSRPS required to transform the input sequence into a constant sequence. We test this measure on symbolic sequences of the Logistic map for various values of the bifurcation parameter. The proposed measure of complexity is easy to compute and is observed to be highly correlated with the Lyapunov exponent of the original non-linear time series, even for very short symbolic sequences (as short as 50 samples). Finally, we construct symbolic sequences from the Skew-Tent map which are incompressible by popular compression algorithms like WinZip, WinRAR and 7-Zip, but compressible by NSRPS.