Complexity-Theoretic Aspects of Expanding Cellular Automata

Augusto Modanese

doi:10.1007/s11047-020-09814-2

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arXiv · 1902.05487

Complexity-Theoretic Aspects of Expanding Cellular Automata

Augusto Modanese

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Abstract

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 ${\le_{tt}^p}(\mathsf{NP})$, that is, the class of decision problems polynomial-time truth-table reducible to problems in $\mathsf{NP}$. 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 ${\le_{tt}^p}(\mathsf{NP})$ and the Turing machine polynomial-time class $\mathsf{P}$.

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BibTeX RIS

Augusto Modanese. 2019-02-14. Complexity-Theoretic Aspects of Expanding Cellular Automata. https://doi.org/10.1007/s11047-020-09814-2

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