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Complexity-theoretic aspects of expanding cellular automata

2020; Springer Science+Business Media; Volume: 21; Issue: 1 Linguagem: Inglês

10.1007/s11047-020-09814-2

1572-9796

Augusto Modanese,

DNA and Biological Computing

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 $\mathsf{P}$.