Complexity-Theoretic Aspects of Expanding Cellular Automata

02/14/2019

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by   Augusto Modanese, et al.

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The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. The respective polynomial-time complexity class is shown to coincide with <_tt^p(NP), that is, the class of decision problems polynomial-time truth-table reducible to problems in NP. Corollaries on select XCA variants are proven: XCAs with multiple accept and reject states are shown to be polynomial-time equivalent to the original XCA model. Meanwhile, XCAs with diverse acceptance behavior are classified in terms of <_tt^p(NP) and the Turing machine polynomial-time class P.