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A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
A Padding Technique on Cellular Automata to Transfer Inclusions of Complexity Classes
"... Abstract. We will show how padding techniques can be applied on onedimensional cellular automata by proving a transfer theorem on complexity classes (how one inclusion of classes implies others). Then we will discuss the consequences of this result, in particular when considering that all languages ..."
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Abstract. We will show how padding techniques can be applied on onedimensional cellular automata by proving a transfer theorem on complexity classes (how one inclusion of classes implies others). Then we will discuss the consequences of this result, in particular when considering that all languages recognized in linear space can be recognized in linear time (whether or not this is true is still an open question), and see the implications on onetape Turing machines. 1
Separating RealTime and Linear Space Recognition of Languages on OneDimensional Cellular Automata
, 2006
"... In this article we will focus on a famous open question about algorithmic complexity classes on one dimensional cellular automata, and we will show that if all problems recognizable in space n (where n is the length of the input) can be recognized in time n then for every spaceconstructible functio ..."
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In this article we will focus on a famous open question about algorithmic complexity classes on one dimensional cellular automata, and we will show that if all problems recognizable in space n (where n is the length of the input) can be recognized in time n then for every spaceconstructible function f all the problems that are recognizable in space f can be recognized in time f.