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The light lexicographic path ordering
, 2000
"... We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space bounded by a polynomial in the size of the inputs. 1 ..."
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We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space bounded by a polynomial in the size of the inputs. 1
Iterative Lexicographic Path Orders
"... Abstract. We relate Kamin and Lévy’s original presentation of lexicographic path orders (LPO), using an inductive definition, to a presentation, which we will refer to as iterative lexicographic path orders (ILPO), based on Bergstra and Klop’s definition of recursive path orders by way of an auxilia ..."
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Abstract. We relate Kamin and Lévy’s original presentation of lexicographic path orders (LPO), using an inductive definition, to a presentation, which we will refer to as iterative lexicographic path orders (ILPO), based on Bergstra and Klop’s definition of recursive path orders by way
Lexicographic Path Induction
"... Abstract. Programming languages theory is full of problems that reduce to proving the consistency of a logic, such as the normalization of typed lambdacalculi, the decidability of equality in type theory, equivalence testing of traces in security, etc. Although the principle of transfinite inductio ..."
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induction is routinely employed by logicians in proving such theorems, it is rarely used by programming languages researchers who often prefer alternatives such as proofs by logical relations and model theoretic constructions. In this paper we harness the wellfoundedness of the lexicographic path ordering
Skipnet: A scalable overlay network with practical locality properties
, 2003
"... Abstract: Scalable overlay networks such as Chord, Pastry, and Tapestry have recently emerged as a flexible infrastructure for building large peertopeer systems. In practice, two disadvantages of such systems are that it is difficult to control where data is stored and difficult to guarantee that ..."
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Cited by 359 (5 self)
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that routing paths remain within an administrative domain. SkipNet is a scalable overlay network that provides controlled data placement and routing locality guarantees by organizing data primarily by lexicographic key ordering. SkipNet also allows for both finegrained and coarsegrained control over data
Lexicographic products in metarouting
, 2007
"... Routing protocols often keep track of multiple route metrics, where some metrics are more important than others. Route selection is then based on lexicographic comparison: the most important attribute of each route is considered first, and if this does not give enough information to decide which rou ..."
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Cited by 13 (6 self)
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route is better, the next attribute is considered; and so on. We investigate protocols that find globally optimal paths and protocols that find only locally optimal paths. In each case we characterize exactly when lexicographic products can be used to define wellbehaved routing protocols. We apply our
Nonrepetitive colorings of lexicographic product of paths and other graphs
, 2013
"... A coloring c of the vertices of a graph G is nonrepetitive if there exists no path v1v2... v2l for which c(vi) = c(vl+i) for all 1 ≤ i ≤ l. Given graphs G and H with V (H)  = k, the lexicographic product G[H] is the graph obtained by substituting every vertex ofG by a copy ofH, and every edge of ..."
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A coloring c of the vertices of a graph G is nonrepetitive if there exists no path v1v2... v2l for which c(vi) = c(vl+i) for all 1 ≤ i ≤ l. Given graphs G and H with V (H)  = k, the lexicographic product G[H] is the graph obtained by substituting every vertex ofG by a copy ofH, and every edge
Absorbing Lexicographic Products in Metarouting
"... Abstract—Modern treatments of routing protocols use algebraic techniques to derive the protocol’s properties, permitting a semantic richness more flexible than simple numerical “shortest paths”. Many such routing protocols make preference decisions based on multiple criteria. This fits well with an ..."
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Abstract—Modern treatments of routing protocols use algebraic techniques to derive the protocol’s properties, permitting a semantic richness more flexible than simple numerical “shortest paths”. Many such routing protocols make preference decisions based on multiple criteria. This fits well
9 SpringerVerlag 1989 Lexicographic Monotone Path Solutions
, 1987
"... Summary. The family of 2person bargaining solutions called Lexicographic monotone path solutions which are nonsymmetric generalizations of the lexicographic egalitarian solution is characterized in several ways. Central in these characterizations is an interiority condition first introduced in [ ..."
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Summary. The family of 2person bargaining solutions called Lexicographic monotone path solutions which are nonsymmetric generalizations of the lexicographic egalitarian solution is characterized in several ways. Central in these characterizations is an interiority condition first introduced
A New Method for Undecidability Proofs of First Order Theories
 Journal of Symbolic Computation
, 1992
"... this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction ..."
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Cited by 30 (6 self)
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this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction
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