3 research outputs found

    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. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with ≀ttp(NP){\le_{tt}^p}(\mathsf{NP}), that is, the class of decision problems polynomial-time truth-table reducible to problems in NP\mathsf{NP}. An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, 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. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of ≀ttp(NP){\le_{tt}^p}(\mathsf{NP}) and the Turing machine polynomial-time class P\mathsf{P}.Comment: 19 pages, 3 figure

    Complexity-theoretic aspects of expanding cellular automata

    Get PDF
    The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with ≀ttp≀^{p}_{tt}(NP), that is, the class of decision problems polynomial-time truth-table reducible to problems in NP. An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, 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. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of ≀ttp≀^{p}_{tt}(NP) and the Turing machine polynomial-time class P
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