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A DegreeDecreasing Lemma for (MOD q  MOD p) Circuits
, 2001
"... plus an arbitrary linear function of n input variables. Keywords: Circuit complexity, modular circuits, composite modulus 1 Introduction Boolean circuits are one of the most interesting models of computation. They are widely examined in VLSI design, in general computability theory and in complexit ..."
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plus an arbitrary linear function of n input variables. Keywords: Circuit complexity, modular circuits, composite modulus 1 Introduction Boolean circuits are one of the most interesting models of computation. They are widely examined in VLSI design, in general computability theory and in complexity theory context as well as in the theory of parallel computation. Almost all of the strongest and deepest lower bound results for the computational complexity of finite functions were proved using the Boolean circuit model of computation ([13], [22], [9], [14], [15], or see [20] for a survey). Even these famous and sophisticated lower bound results were proven for very restricted circuit classes. Bounded depth and polynomial size is one of the most natural restrictions. Ajtai [1], Furst, Saxe, and Sipser [5] proved that no polynomial sized, constant depth circuit can compute the PARITY function. Yao [22] and Hastad [9] generalized this result
Quantum Computation and Shor's Factoring Algorithm
, 1999
"... The field of quantum computation studies the power of computers that are based on quantummechanical principles. We give a brief introduction to the model of quantum computation and to its main success so far: Peter Shor's efficient quantum algorithm for factoring integers. 1 Introduction Today's co ..."
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The field of quantum computation studies the power of computers that are based on quantummechanical principles. We give a brief introduction to the model of quantum computation and to its main success so far: Peter Shor's efficient quantum algorithm for factoring integers. 1 Introduction Today's computersboth in theory (Turing machines) and practice (PCs)are based on classical physics. They are limited by locality (operations have only local effects) and by the classical fact that systems can be in only one state at the time. However, modern quantum physics tells us that the world behaves quite differently: some operations can have nonlocal effects and in some sense quantum systems can be in several states simultaneously. Quantum computation is the field that investigates the computational power and other properties of computers based on quantummechanical principles. Its main objective is to find quantum algorithms that are significantly faster than any classical algorithm so...
SEMANTICS FOR MULTIRATE FAUST
"... Abstract. Faust is a functional programming language dedicated to the specification of executable monorate musical applications. We present here a multirate extension of the core of the Faust language, called MR Faust, together with a typing semantics, a denotational semantics and correctness theore ..."
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Abstract. Faust is a functional programming language dedicated to the specification of executable monorate musical applications. We present here a multirate extension of the core of the Faust language, called MR Faust, together with a typing semantics, a denotational semantics and correctness theorems that link them together. 1.
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"... Unité de recherche associée au CNRS n°1398 On the relations between dynamical systems and boolean circuits ..."
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Unité de recherche associée au CNRS n°1398 On the relations between dynamical systems and boolean circuits
Design and Implementation of 8½, a Declarative DataParallel Language
 Computer Languages
, 1995
"... 8 ½, an experimental language combining features of collection and stream oriented languages... ..."
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8 ½, an experimental language combining features of collection and stream oriented languages...
Average case reductions for Subset Sum and Decoding of Linear Codes
, 1999
"... Average case reductions for Subset Sum and Decoding of Linear Codes Genevi`eve Arboit Master of Science Graduate Department of Computer Science University of Toronto 1999 In a 1996 paper, R. Impagliazzo and M. Naor show two average case reductions for the Subset Sum problem (SS). We use similar idea ..."
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Average case reductions for Subset Sum and Decoding of Linear Codes Genevi`eve Arboit Master of Science Graduate Department of Computer Science University of Toronto 1999 In a 1996 paper, R. Impagliazzo and M. Naor show two average case reductions for the Subset Sum problem (SS). We use similar ideas to obtain stronger and additional such reductions for SS. Furthermore, we use modifications of these ideas to obtain similar reductions for the Decoding of Linear Codes problem (DLC). The theorems give further evidence that the hardest case for Average case SS is when the number of integers is equal to their length. For Average case DLC, the theorems give evidence that the hardest case is when the dimension of the code is equal to the channel capacity times the length of the words. Average case SS and DLC hardness assumptions can be used to obtain oneway functions, pseudorandom generators, and secure privatekey cryptography. ii Acknowledgments I dedicate this work to my parents, who ha...
Cost vs. Quality: Tradeoffs in Communication Networks
, 2000
"... 1 List of Figures 3 List of Terms 5 1 Introduction 6 1.1 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 The Virtual Topology Design Problem in AllOptical Networks : : : : : : : : 8 1.2.1 Background, Definitions and Goals : : : : : : : : : : : : : : : : : : ..."
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1 List of Figures 3 List of Terms 5 1 Introduction 6 1.1 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 The Virtual Topology Design Problem in AllOptical Networks : : : : : : : : 8 1.2.1 Background, Definitions and Goals : : : : : : : : : : : : : : : : : : : 8 1.2.2 Contribution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 1.3 The Design of Routing Strategies : : : : : : : : : : : : : : : : : : : : : : : : 13 1.3.1 Background, Definitions, and Goals : : : : : : : : : : : : : : : : : : : 13 1.3.2 Contribution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 1.4 Published Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 16 1.5 Organization of the Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : 16 I The Design of the Virtual Topology 17 2 A Formal Model 18 2.1 Survivability and the Layered Hierarchy : : : : : : : : : : : : : : : : : : : : 18 2.2 Survivability within the Opti...
A Theory Repository On The Web: A Proposal
, 2000
"... Introduction There are now numerous sites on the web that contain useful information for theoretical computer scientists. Among the more popular sites are those maintaining bibliographies and surveys for specic subject areas; many journals and conferences now maintain an online presence as well, al ..."
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Introduction There are now numerous sites on the web that contain useful information for theoretical computer scientists. Among the more popular sites are those maintaining bibliographies and surveys for specic subject areas; many journals and conferences now maintain an online presence as well, allowing easy access to published papers. It is now common to perform literature searches directly on the web, as well as on specialized databases like INSPEC. There are sites that maintain links for specic subject areas [3, 5, 7], as well as sites that maintain information about conference announcements and deadlines [24, 7, 13]. In addition, there are paper and bibliography databases like the Hypertext Bibliography Project [14], the Computing Research Repository [17], and the Computer Science Research Paper Search Engine [19]. Searching for relevant material however is still a timeconsuming task, given the volume of information available and the lack of contextual precision of mo
Chapter 1 Efficient Algorithms
"... For me, great algorithms are the poetry of computation. Just like verse, they can be terse, allusive, dense, and even mysterious. But once unlocked, they cast a brilliant new light on some aspect of computing. ..."
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For me, great algorithms are the poetry of computation. Just like verse, they can be terse, allusive, dense, and even mysterious. But once unlocked, they cast a brilliant new light on some aspect of computing.