Complexity-Theoretic Aspects of Expanding Cellular Automata
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 $\mathsf{P}$.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.05487
- arXiv:
- arXiv:1902.05487
- Bibcode:
- 2019arXiv190205487M
- Keywords:
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- Computer Science - Computational Complexity;
- Computer Science - Formal Languages and Automata Theory;
- Mathematics - Dynamical Systems
- E-Print:
- 19 pages, 3 figures