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}(textsf {NP}), that is, the class of decision problems polynomial-time truth-table reducible to problems in textsf {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}(textsf {NP}) and the Turing machine polynomial-time class textsf {P}.
Highlights
Cellular automata (CAs) are defined as a rigid and immutable lattice of cells; their behavior is dictated exclusively by a local transition function operating on homogeneous local configurations
The following generalizes STATE8 to the case of multiple accept-reject XCA (MAR-XCA): Definition 16 (STATEM8 AR) Let A be an MAR-XCA with state set Q, and let VA be the set of triples (w, t, Z), w being an input for A, t 2 f0; 1gþ a binary encoding of s 2 N0, and Z Q
It was shown that the polynomial-time class EXCAP equals XCAP (Theorem 20); in the latter, it was shown that the polynomial-time class
Summary
Cellular automata (CAs) are defined as a rigid and immutable lattice of cells; their behavior is dictated exclusively by a local transition function operating on homogeneous local configurations. This can be generalized, for instance, by mutable neighborhoods (Rosenfeld and Wu 1981) or by endowing CAs with the ability to shrink, that is, delete their cells (Rosenfeld et al 1983). In the one-dimensional case, further variants in this sense are considered in the work of Dubacq (1994), where one finds, in particular, CAs whose neighborhoods vary over time. An additional example of cell division in this sense is the ‘‘inflating grid’’ of Arrighi and Dowek (2013)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
