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415
Software Watermarking: Models and Dynamic Embeddings
, 1999
"... Watermarking embeds a secret message into a cover message. In media watermarking the secret is usually a copyright notice and the cover a digital image. Watermarking an object discourages intellectual property theft, or when such theft has occurred, allows us to prove ownership. The Software Waterma ..."
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Cited by 161 (21 self)
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Watermarking embeds a secret message into a cover message. In media watermarking the secret is usually a copyright notice and the cover a digital image. Watermarking an object discourages intellectual property theft, or when such theft has occurred, allows us to prove ownership. The Software Watermarking problem can be described as follows. Embed a structure W into a program P such that: W can be reliably located and extracted from P even after P has been subjected to code transformations such as translation, optimization and obfuscation; W is stealthy; W has a high data rate; embedding W into P does not adversely affect the performance of P ; and W has a mathematical property that allows us to argue that its presence in P is the result of deliberate actions. In the first part of the paper we construct an informal taxonomy of software watermarking techniques. In the second part we formalize these results. Finally, we propose a new software watermarking technique in which a dynamic gr...
Spiders for rank 2 Lie algebras
 Commun. Math. Phys
, 1996
"... Abstract. A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or grouplike object. It is also known as a spherical category, or a strict, monoidal category with a few extra properties, or by several other names. A recently useful point o ..."
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Cited by 122 (2 self)
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Abstract. A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or grouplike object. It is also known as a spherical category, or a strict, monoidal category with a few extra properties, or by several other names. A recently useful point of view, developed by other authors, of the representation theory of sl(2) has been to present it as a spider by generators and relations. That is, one has an algebraic spider, defined by invariants of linear representations, and one identifies it as isomorphic to a combinatorial spider, given by generators and relations. We generalize this approach to the rank 2 simple Lie algebras, namely A2, B2, and G2. Our combinatorial rank 2 spiders yield bases for invariant spaces which are probably related to Lusztigâ€™s canonical bases, and they are useful for computing quantities such as generalized 6jsymbols and quantum link invariants. Their definition originates in definitions of the rank 2 quantum link invariants that were discovered independently by the author and Francois Jaeger. 1.
Random Mapping Statistics
 IN ADVANCES IN CRYPTOLOGY
, 1990
"... Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of ..."
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Cited by 110 (6 self)
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Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of about twenty characteristic parameters of random mappings is carried out: These parameters are studied systematically through the use of generating functions and singularity analysis. In particular, an open problem of Knuth is solved, namely that of finding the expected diameter of a random mapping. The same approach is applicable to a larger class of discrete combinatorial models and possibilities of automated analysis using symbolic manipulation systems ("computer algebra") are also briefly discussed.
Boltzmann Samplers For The Random Generation Of Combinatorial Structures
 Combinatorics, Probability and Computing
, 2004
"... This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combina ..."
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Cited by 108 (3 self)
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This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class  an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on realarithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.
The enumeration of fully commutative elements of Coxeter groups
 J. Algebraic Combin
, 1998
"... Abstract. Let W be a Coxeter group. We define an element w ~ W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting generators. We give several combinatorial characterizations of this property, classify the Cox ..."
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Cited by 106 (4 self)
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Abstract. Let W be a Coxeter group. We define an element w ~ W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting generators. We give several combinatorial characterizations of this property, classify the Coxeter groups with finitely many fully commutative elements, and classify the parabolic quotients whose members are all fully commutative. As applications of the latter, we classify all parabolic quotients with the property that (1) the Bruhat ordering is a lattice, (2) the Bruhat ordering is a distributive lattice, (3) the weak ordering is a distributive lattice, and (4) the weak ordering and Bruhat ordering coincide.
AverageCase Analysis of Algorithms and Data Structures
, 1990
"... This report is a contributed chapter to the Handbook of Theoretical Computer Science (NorthHolland, 1990). Its aim is to describe the main mathematical methods and applications in the averagecase analysis of algorithms and data structures. It comprises two parts: First, we present basic combinato ..."
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Cited by 105 (8 self)
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This report is a contributed chapter to the Handbook of Theoretical Computer Science (NorthHolland, 1990). Its aim is to describe the main mathematical methods and applications in the averagecase analysis of algorithms and data structures. It comprises two parts: First, we present basic combinatorial enumerations based on symbolic methods and asymptotic methods with emphasis on complex analysis techniques (such as singularity analysis, saddle point, Mellin transforms). Next, we show how to apply these general methods to the analysis of sorting, searching, tree data structures, hashing, and dynamic algorithms. The emphasis is on algorithms for which exact "analytic models" can be derived.
Infinite wedge and random partitions
 Selecta Mathematica (new series
"... The aim of this paper is to show that random partitions have a very natural and direct connection to various structures which are well known in integrable systems. This connection is arguably even more natural than, for example, ..."
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Cited by 96 (7 self)
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The aim of this paper is to show that random partitions have a very natural and direct connection to various structures which are well known in integrable systems. This connection is arguably even more natural than, for example,
Periods in strings
 Journal of Combinatorial Theory, Series A
, 1981
"... A survey is presented of some methods and results on counting words that satisfy various restrictions on subwords (i.e., blocks of consecutive symbols). Various applications to commafree codes, games, pattern matching, and other subjects are indicated. The emphasis is on the unified treatment of th ..."
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Cited by 92 (0 self)
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A survey is presented of some methods and results on counting words that satisfy various restrictions on subwords (i.e., blocks of consecutive symbols). Various applications to commafree codes, games, pattern matching, and other subjects are indicated. The emphasis is on the unified treatment of those topics through the use of generating functions. 1.