3 research outputs found
Complexity-Theoretic Aspects of Expanding Cellular Automata
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 , that is, the class of decision
problems polynomial-time truth-table reducible to problems in . 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
and the Turing machine polynomial-time class
.Comment: 19 pages, 3 figure
Complexity-theoretic aspects of expanding cellular automata
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 (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 (NP) and the Turing machine polynomial-time class P