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264
Topological Equivalence of Tilings
 J.MATH.PHYS., VOL
, 1997
"... We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are topologically equivalent whenever their associated groupoids are isomor ..."
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Cited by 25 (7 self)
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We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are topologically equivalent whenever their associated groupoids
The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 72 (27 self)
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by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences
Tiling the Line with Translates of One Tile
, 1995
"... This paper shows for a bounded tile that all tilings it gives of R are periodic, and that there are finitely many translationequivalence classes of such tilings. The main result of the paper is that for any tiling of R by a bounded tile, any two tiles in the tiling differ by a rational multiple of ..."
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Cited by 56 (8 self)
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This paper shows for a bounded tile that all tilings it gives of R are periodic, and that there are finitely many translationequivalence classes of such tilings. The main result of the paper is that for any tiling of R by a bounded tile, any two tiles in the tiling differ by a rational multiple
Tiling Multidimensional Iteration Spaces for Multicomputers
, 1992
"... This paper addresses the problem of compiling perfectly nested loops for multicomputers (distributed memory machines). The relatively high communication startup costs in these machines renders frequent communication very expensive. Motivated by this, we present a method of aggregating a number of lo ..."
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Cited by 109 (21 self)
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. Since synchronization is not allowed during the execution of a tile, partitioning the iteration space into tiles must not result in deadlock. We first show the equivalence between the problem of finding partitions and the problem of determining the cone for a given set of dependence vectors. We
Tiling groups for Wang tiles
 PROCEEDINGS OF THE 13 TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA) SIAM EDS
"... We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group. For al ..."
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Cited by 7 (4 self)
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We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group
A variational principle for domino tilings
"... Abstract. We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can be described by a function that maximizes an entrop ..."
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Cited by 104 (16 self)
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Abstract. We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can be described by a function that maximizes
TILING THE INTEGERS WITH APERIODIC TILES
"... Abstract. A finite subset A of integers tiles the discrete line Z if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile the integers are known. We extend this result to a large class of nonperiodic tilings and give a n ..."
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Cited by 1 (0 self)
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Abstract. A finite subset A of integers tiles the discrete line Z if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile the integers are known. We extend this result to a large class of nonperiodic tilings and give a
Groups and Tilings
, 2001
"... We prove that the word problem for the group of dominoes is equivalent to the existence of a directed tiling for the corresponding closed curve in the plane, which, in turns is equivalent to the fact that the curve is "balanced". This last property beeing decidable, the word problem is als ..."
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We prove that the word problem for the group of dominoes is equivalent to the existence of a directed tiling for the corresponding closed curve in the plane, which, in turns is equivalent to the fact that the curve is "balanced". This last property beeing decidable, the word problem
Tiles for Reo
 Recent Trends in Algebraic Development Techniques, pages 37–55. LNCS 5486
, 2009
"... Abstract. Reo is an exogenous coordination model for software components. The informal semantics of Reo has been matched by several proposals of formalization, exploiting coalgebraic techniques, constraintautomata, and coloring tables. We aim to show that the Tile Model offers a flexible and ade ..."
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Cited by 9 (5 self)
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Abstract. Reo is an exogenous coordination model for software components. The informal semantics of Reo has been matched by several proposals of formalization, exploiting coalgebraic techniques, constraintautomata, and coloring tables. We aim to show that the Tile Model offers a flexible
Tiling threespace by combinatorially equivalent convex polytopes
 Proc. London Math. Soc
, 1984
"... The paper settles a problem of Danzer, Griinbaum, and Shephard on tilings by convex polytopes. We prove that, for a given threedimensional convex polytope P, there is a locally finite tiling of the Euclidean threespace by convex polytopes each combinatorially equivalent to P. In general, facetof ..."
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Cited by 7 (4 self)
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The paper settles a problem of Danzer, Griinbaum, and Shephard on tilings by convex polytopes. We prove that, for a given threedimensional convex polytope P, there is a locally finite tiling of the Euclidean threespace by convex polytopes each combinatorially equivalent to P. In general, face
Results 1  10
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264