Two Results on Polynomial Time Truth-Table Reductions to Sparse Sets

1983 ◽  
Vol 12 (3) ◽  
pp. 580-587 ◽  
Author(s):  
Esko Ukkonen
Keyword(s):  
2020 ◽  
Author(s):  
Augusto Modanese

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 $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) , that is, the class of decision problems polynomial-time truth-table reducible to problems in $$\textsf {NP}$$ 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 $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) and the Turing machine polynomial-time class $$\textsf {P}$$ P .


2002 ◽  
Vol 35 (4) ◽  
pp. 449-463 ◽  
Author(s):  
Shin Aida ◽  
Rainer Schuler ◽  
Tatsuie Tsukiji ◽  
Osamu Watanabe

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