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In Some Curved Spaces, One Can Solve NPHard Problems in Polynomial Time
"... In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved s ..."
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Cited by 6 (6 self)
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In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NPhard. It is well known that many important practical problems are NPhard; see, e.g., [11, 14, 27]. Under the usual hypothesis that P̸=NP, NPhardness has the following intuitive meaning: every algorithm which solves all instances of the corresponding problem requires, for
The Domino Problem of the Hyperbolic Plane is Undecidable
 Bulletin of the EATCS
, 2007
"... In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the g ..."
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Cited by 5 (4 self)
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In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966. 1
Navigation in tilings of the hyperbolic plane and possible applications
, 909
"... Abstract—This paper introduces a method of navigation in a large family of tilings of the hyperbolic plane and looks at the question of possible applications in the light of the few ones which were already obtained. ..."
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Abstract—This paper introduces a method of navigation in a large family of tilings of the hyperbolic plane and looks at the question of possible applications in the light of the few ones which were already obtained.
unknown title
, 2008
"... About the domino problem in the hyperbolic plane, a new solution: complement ..."
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About the domino problem in the hyperbolic plane, a new solution: complement
unknown title
, 2008
"... About the domino problem in the hyperbolic plane, a new solution: complement ..."
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About the domino problem in the hyperbolic plane, a new solution: complement
unknown title
, 2008
"... About the domino problem in the hyperbolic plane, a new solution: complement ..."
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About the domino problem in the hyperbolic plane, a new solution: complement