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Recursive Construction
, 2015
"... Let S be a specification in state variables σ (in mathematical variables σ and σʹ ′), not including a time variable, such that (0) ∀σ · ∃σʹ′ · S “ S is implementable” (1) ∀σ · ∃σʹ′ · ¬S “ ¬S is implementable” For example, S could be xʹ′=0. Define (2) D = if ∀σ, σʹ′ · S⇐D then ¬S else S f ..."
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Let S be a specification in state variables σ (in mathematical variables σ and σʹ ′), not including a time variable, such that (0) ∀σ · ∃σʹ′ · S “ S is implementable” (1) ∀σ · ∃σʹ′ · ¬S “ ¬S is implementable” For example, S could be xʹ′=0. Define (2) D = if ∀σ, σʹ′ · S⇐D then ¬S else S fi The ifpart, ∀σ, σʹ′ · S⇐D , says that D is an implementation of S. It has no nonlocal variables; either it is the constant ⊤ or it is the constant ⊥. Suppose is it ⊤. Then ⊤ assumption and (2) = (∀σ, σʹ′ · S⇐D) ∧ (∀σ, σʹ′ · D = if ∀σ, σʹ′ · S⇐D then ¬S else S fi) context ⇒ (∀σ, σʹ′ · S⇐D) ∧ (∀σ, σʹ′ · D = ¬S) splitting = ∀σ, σʹ′ · (S⇐D) ∧ (D = ¬S) ⇒ ∀σ, σʹ′ · S add (1) = (∀σ, σʹ′ · S) ∧ (∀σ · ∃σʹ′ · ¬S) Suppose ∀σ, σʹ′ · S⇐D is ⊥. Then ⊤ assumption and (2) = ¬(∀σ, σʹ′ · S⇐D) ∧ (∀σ, σʹ′ · D = if ∀σ, σʹ′ · S⇐D then ¬S else S fi) context = ¬(∀σ, σʹ′ · S⇐D) ∧ (∀σ, σʹ′ · D=S) We have an inconsistency, introduced by definition (2). Assumption (0) is needed so that it is sensible to talk about implementing specification S. Assumption (1) is needed to prove that (2) is an inconsistent definition.
Recursive constructions for triangulations
 J. Graph Theory
"... This is a preprint of an article accepted for publication in the Journal of Graph Theory c©2001 (copyright owner as specified in the journal). Three recursive constructions are presented; two deal with embeddings of complete graphs and one with embeddings of complete tripartite graphs. All three fa ..."
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Cited by 12 (10 self)
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This is a preprint of an article accepted for publication in the Journal of Graph Theory c©2001 (copyright owner as specified in the journal). Three recursive constructions are presented; two deal with embeddings of complete graphs and one with embeddings of complete tripartite graphs. All three
Recursive Constructions of Complete Caps
"... We present three constructions of complete caps in PG(d; q), q odd, where complete caps in a projective space of smaller dimension are involved. We thereby obtain new series of upper bounds on n 2 (d; q), the smallest number of points in a complete cap in PG(d; q). The constructions show that fo ..."
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Cited by 3 (1 self)
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We present three constructions of complete caps in PG(d; q), q odd, where complete caps in a projective space of smaller dimension are involved. We thereby obtain new series of upper bounds on n 2 (d; q), the smallest number of points in a complete cap in PG(d; q). The constructions show
NonRecursively Constructible Recursive Families of Graphs
, 2012
"... In a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjectu ..."
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Cited by 2 (0 self)
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In a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples
Solving Problems on Recursively Constructed Graphs
"... Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed. This paper first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive gr ..."
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Cited by 5 (0 self)
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Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed. This paper first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive
Recursive Construction of Granular Route Directions
 Journal of Spatial Science
, 2006
"... People give route directions to persons who are familiar with the environment typically by refering to elements of the city of varying granularitywhat we call granular route directions. This is in contrast to current navigation services, which produce directions of constant granularity. In granul ..."
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Cited by 11 (4 self)
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directions can be automatically constructed by selecting appropriate elements of the city from a hierarchical city structure, and we further demonstrate that the process is based on a recursive application of a small set of topological rules.
The Hausdorff dimension of some snowflakelike recursive constructions
, 2011
"... Fractal subsets of Rn with highly regular structure are often constructed as a limit of a recursive procedure based on contractive maps. The Hausdorff dimension of recursively constructed fractals is relatively easy to find when the contractive maps associated with each recursive step satisfy the Op ..."
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Fractal subsets of Rn with highly regular structure are often constructed as a limit of a recursive procedure based on contractive maps. The Hausdorff dimension of recursively constructed fractals is relatively easy to find when the contractive maps associated with each recursive step satisfy
Some Recursive Constructions for Perfect Hash Families
 JOURNAL OF COMBINATORIAL DESIGNS
, 1996
"... An (n; m;w)perfect hash family is a set of functions F such that f : f1; : : : ; ng ! f1; : : : ; mg for each f 2 F , and for any X ` f1; : : : ; ng such that jX j = w, there exists at least one f 2 F such that f j X is onetoone. Perfect hash families have been extensively studied by computer s ..."
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Cited by 27 (10 self)
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scientists for over 15 years, mainly due to their applications in database management. In particular, much attention has been given to finding efficient algorithms to construct perfect hash families. In this paper, we study perfect hash families from a combinatorial viewpoint, and describe some new recursive
Novel recursive construction method for resilient Sboxes
"... Abstract. Resilient Sboxes have many applications in quantum cryptographic key distribution, random sequence generation for stream ciphers, and faulttolerant distributed computing. In this paper, we provide a novel method of constructing new resilient Sboxes from old ones. The proposed method is ..."
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is a simple modification on the recursive construction technique for resilient Sboxes due to Zhang and Zheng. The modified ZhangZheng construction has better performance since it increases the output dimensions of Sboxes, whereas having the same resiliency as the existing method. Using this new
Results 1  10
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