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**21 - 28**of**28**### 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 time-consuming 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.

### LIP

"... 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

### 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 one-way functions, pseudorandom generators, and secure private-key cryptography. ii Acknowledgments I dedicate this work to my parents, who ha...

### Design and Implementation of 8½, a Declarative Data-Parallel 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...

### The Thompson-Higman monoids Mk,i: the J-order, the D-relation, and their complexity

, 2009

"... The Thompson-Higman groups Gk,i have a natural generalization to monoids, called Mk,i, and inverse monoids, called Invk,i. We study some structural features of Mk,i and Invk,i and investigate the computational complexity of related decision problems. The main interest of these monoids is their close ..."

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The Thompson-Higman groups Gk,i have a natural generalization to monoids, called Mk,i, and inverse monoids, called Invk,i. We study some structural features of Mk,i and Invk,i and investigate the computational complexity of related decision problems. The main interest of these monoids is their close connection with circuits and circuit complexity. The maximal subgroups of Mk,1 and Invk,1 are isomorphic to the groups Gk,j (1 ≤ j ≤ k − 1); so we rediscover all the Thompson-Higman groups within Mk,1. Deciding the Green relations ≤J and ≡D of Mk,1, when the inputs are words over a finite generating set of Mk,1, is in P. When a circuit-like generating set is used for Mk,1 then deciding ≤J is coDP-complete (where DP is the complexity class consisting of differences of sets in NP). The multiplier search problem for ≤J is xNPsearch-complete, whereas the multiplier search problems of ≤R and ≤L are not in xNPsearch unless NP = coNP. We introduce the class of search problems xNPsearch as a slight generalization of NPsearch. Deciding ≡D for Mk,1 when the inputs are words over a circuit-like generating set, is ⊕k−1•NPcomplete; for any h ≥ 2, ⊕h•NP is a modular counting complexity class, whose verification problems are in NP. Related problems for partial circuits are the image size problem (which is # • NPcomplete), and the image size modulo h problem (which is ⊕h •NP-complete). For Invk,1 over a circuit-like generating set, deciding ≡D is ⊕k−1P-complete. It is interesting that the little known complexity classes coDP and ⊕k−1•NP play a central role in Mk,1.