Shrinking and Expanding Cellular Automata

Abstract : Inspired by shrinking cellular automata (SCA), we investigate another variant of the classical one-dimensional cellular automaton: the shrinking and expanding cellular automaton (SXCA). In addition to the capability to delete some cells as in SCA, an SXCA can also create new cells between already existing ones. It is shown that there are reasonably close (polynomial) relations between the time complexity of SXCA and the space and time complexity of Turing machines and alternating Turing machines respectively. As a consequence the class of problems decidable in polynomial time by SXCA coincides with PSPACE.
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Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Lecture Notes in Computer Science, LNCS-9664, pp.159-169, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_13〉
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Augusto Modanese, Thomas Worsch. Shrinking and Expanding Cellular Automata. Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Lecture Notes in Computer Science, LNCS-9664, pp.159-169, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_13〉. 〈hal-01435026〉

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