5 research outputs found
Dynamic neighbourhood cellular automata.
We propose a definition of cellular automaton in which each cell can change its neighbourhood during a computation. This is done locally by looking not farther than neighbours of neighbours and the number of links remains bounded by a constant throughout. We suggest that dynamic neighbourhood cellular automata can serve as a theoretical model in studying algorithmic and computational complexity issues of ubiquitous computations. We illustrate our approach by giving an optimal, logarithmic time solution of the Firing Squad Synchronization problem in this setting
Dynamic Neighbourhood Cellular Automata
We propose a definition of cellular automaton in which each cell can change its neighbourhood during a computation. This is done locally by looking not farther than neighbours of neighbours and the number of links remains bounded by a constant throughout. We suggest that dynamic neighbourhood cellular automata can serve as a theoretical model in studying algorithmic and computational complexity issues of ubiquitous computations. We illustrate our approach by giving an optimal, logarithmic time solution of the Firing Squad Synchronization problem in this setting
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