{"abstract":"In this dissertation, we study two of the global properties of 1-dimensional\ncellular automata (CAs) under periodic boundary condition, namely,\nreversibility and randomness. To address reversibility of finite CAs, we\ndevelop a mathematical tool, named reachability tree, which can efficiently\ncharacterize those CAs. A decision algorithm is proposed using minimized\nreachability tree which takes a CA rule and size n as input and verifies\nwhether the CA is reversible for that n. To decide reversibility of a finite\nCA, we need to know both the rule and the CA size. However, for infinite CAs,\nreversibility is decided based on the local rule only. Therefore, apparently,\nthese two cases seem to be divergent. This dissertation targets to construct a\nbridge between these two cases. To do so, reversibility of CAs is redefined and\nthe notion of semi-reversible CAs is introduced. Hence, we propose a new\nclassification of finite CAs -(1) reversible CAs, (2) semi-reversible CAs and\n(3) strictly irreversible CAs. Finally, relation between reversibility of\nfinite and infinite CAs is established. This dissertation also explores CAs as\nsource of randomness and build pseudo-random number generators (PRNGs) based on\nCAs. We identify a list of properties for a CA to be a good source of\nrandomness. Two heuristic algorithms are proposed to synthesize candidate\n(decimal) CAs which have great potentiality as PRNGs. Two schemes tare\ndeveloped o use these CAs as window-based PRNGs - (1) as decimal number\ngenerators and as (2) binary number generators. We empirically observe that in\ncomparison to the best PRNG SFMT19937-64, average performance of our proposed\nPRNGs are slightly better. Hence, our decimal CAs based PRNGs are one of the\nbest PRNGs today.","author":[{"family":"Bhattacharjee"}],"id":"unknown","issued":{"date-parts":[[2019,11,9]]},"language":"en","title":"Cellular Automata: Reversibility, Semi-reversibility and Randomness","type":"article"}