Complexity-Theoretic Aspects of Expanding Cellular Automata
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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 Open image in new window , that is, the class of decision problems polynomial-time truth-table reducible to problems in Open image in new window . 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 Open image in new window and the Turing machine polynomial-time class Open image in new window .
The author would like to thank Thomas Worsch for his mentoring, encouragement, and support during the writing of this paper. The author would also like to thank Dennis Hofheinz for pointing out a crucial mistake in a preliminary version of this paper as well as the anonymous referees for their valuable remarks and suggestions.
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