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Quantum hidden subgroup algorithms on free groups, (in preparation
"... Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In thi ..."
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Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor’s quantum factoring algorithm into its basic primitives, then to generalize these primitives, and finally to show how to reassemble them into new QHS algorithms. Taking an ”alphabetic building blocks approach, ” we use these primitives to form an ”algorithmic toolkit ” for the creation of new quantum algorithms, such as wandering Shor algorithms, continuous Shor algorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS algorithm for Feynman integrals, free QHS algorithms, and more. Toward the end of this paper, we show how Grover’s algorithm is most surprisingly “almost ” a QHS algorithm, and how this result suggests the possibility of an even more complete ”algorithmic tookit ” beyond the QHS algorithms. Contents
A CONTINUOUS VARIABLE SHOR ALGORITHM
, 2004
"... Abstract. In this paper, we use the methods found in [21] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → R from the reals R to the reals R, where Φ belongs to a very ge ..."
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Abstract. In this paper, we use the methods found in [21] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → R from the reals R to the reals R, where Φ belongs to a very general class of functions, called the class of admissible functions. One objective in creating this continuous variable quantum algorithm was to make the structure of Shor’s factoring algorithm more mathematically transparent, and thereby give some insight into the inner workings of Shor’s original algorithm. This continuous quantum algorithm also gives some insight into the inner workings of Hallgren’s Pell’s equation algorithm. Two key questions remain unanswered. Is this quantum algorithm more efficient than its classical continuous variable counterpart? Is this quantum
A Novel Balanced Ternary Adder Using Recharged SemiFloating Gate Devices
"... Abstract — This paper presents a novel voltage mode Balanced Ternary Adder (BTA), implemented with Recharged SemiFloating Gate Devices. By using balanced ternary notation, it possible to take advantage of carry free addition, which is exploited in designing a fast adder cell. The circuit operates a ..."
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Abstract — This paper presents a novel voltage mode Balanced Ternary Adder (BTA), implemented with Recharged SemiFloating Gate Devices. By using balanced ternary notation, it possible to take advantage of carry free addition, which is exploited in designing a fast adder cell. The circuit operates at 1 GHz clock frequency. The supply voltage is only 1.0 Volt. The circuit is simulated by using Cadence R○Analog Design Environment, with CMOS090 process parameters, a 90nm General Purpose Bulk CMOS Process from STMicroelectronics with 7 metal layers. All the capacitors are metal plate capacitors, based on vertical coupling capacitance between stacked metal plates. I.
A Novel Ternary More, Less and Equality Circuit Using SemiFloating Gate Devices
 Proceedings IEEE International Symposium on Circuits and Systems
, 2006
"... Abstract — This paper presents a novel Ternary More, Less and Equality (MLE) Circuit implemented with Recharged SemiFloating Gate Transistors. The circuit is a ternary application, and ternary structures may offer the fastest search in a tree structure. The circuit has two ternary inputs, and one t ..."
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Abstract — This paper presents a novel Ternary More, Less and Equality (MLE) Circuit implemented with Recharged SemiFloating Gate Transistors. The circuit is a ternary application, and ternary structures may offer the fastest search in a tree structure. The circuit has two ternary inputs, and one ternary output which will be a comparison of the two ternary inputs. The circuit is a useful building block for use in a search tree application. The circuit is simulated by using Cadence R○Analog Design Environment with CMOS090 GP process parameters from STMicroelectronics, a 90 nm General Purpose Bulk CMOS Process with 7 metal layers. The circuit operates at a 1 GHz clock frequency. The supply voltage is +/ 0.5 Volt. All capacitors are metal plate capacitors, based on a vertical coupling capacitance between stacked metal plates. I.
CloudDT: Efficient Tape Resource Management using Deduplication in Cloud Backup and Archival Services
"... Abstract—Cloudbased backup and archival services use large tape libraries as a costeffective cold tier in their online storage hierarchy today. These services leverage deduplication to reduce the disk storage capacity required by their customer data sets, but they usually reduplicate the data whe ..."
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Abstract—Cloudbased backup and archival services use large tape libraries as a costeffective cold tier in their online storage hierarchy today. These services leverage deduplication to reduce the disk storage capacity required by their customer data sets, but they usually reduplicate the data when moving it from disk to tape. Deduplication does not add significant I/O overhead when performed on disk storage pools. However, when deduplicated data is naively placed on tape storage, the high degree of data fragmentation caused by deduplicationcombined with the high seek and mount times of today's tape technologyleads to high retrieval times. This negatively impacts the recovery time objectives (RTO) that the service provider has to meet as a part of the service level agreement (SLA). This work proposes CloudDT, an extension to Cloud backup and archival services to efficiently support deduplication on tape pools. This paper (i) details the main challenges to enable efficient deduplication on tape libraries, (ii) introduces a class of solutions based on graphmodeling of similarity between data items that enables efficient placement on tapes, and (iii) presents the design and initial evaluation of algorithms that alleviate tape mount time overhead and reduce ontape data fragmentation. Using 4.5 TB of realworld workloads, our initial evaluations show that our algorithms retain at least 95 % of the deduplication storage efficiency, and offer upto 40 % faster restore performance compared to the case of restoring nondeduplicated data. Therefore, our techniques allow the backup service provider to increase tape resource utilization using deduplication, while also improving the restore time performance for the enduser. I.
Do All Roads Lead to Rome? (or Reductions for Dummy Travelers) †
"... Reduction is a central ingredient of computational thinking, and an important tool in algorithm design, in computability theory, and in complexity theory. Reduction has been recognized to be a difficult topic for students to learn. Previous studies on teaching reduction have concentrated on its use ..."
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Reduction is a central ingredient of computational thinking, and an important tool in algorithm design, in computability theory, and in complexity theory. Reduction has been recognized to be a difficult topic for students to learn. Previous studies on teaching reduction have concentrated on its use in special courses on the theory of computing. As a fundamental concept, reduction should be discussed multiple times during a curriculum, starting from firstyear studies. In order to support this, we propose intuitive analogies based on the metaphor of traveling that could be used as an aid for illuminating key ideas of reductions on introductory computer science courses.
Descending chains, the lilypond model
"... and mutual nearest neighbour matching ..."
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DedupT: Deduplication for Tape Systems
"... Abstract—Deduplication is a commonlyused technique on diskbased storage pools. However, deduplication has not been used for tapebased pools: tape characteristics, such as high mount and seek times combined with data fragmentation resulting from deduplication create a toxic combination that leads ..."
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Abstract—Deduplication is a commonlyused technique on diskbased storage pools. However, deduplication has not been used for tapebased pools: tape characteristics, such as high mount and seek times combined with data fragmentation resulting from deduplication create a toxic combination that leads to unacceptably high retrieval times. This work proposes DedupT, a system that efficiently supports deduplication on tape pools. This paper (i) details the main challenges to enable efficient deduplication on tape libraries, (ii) presents a class of solutions based on graphmodeling of similarity between data items that enables efficient placement on tapes; and (iii) presents the design and evaluation of novel crosstape and ontape chunk placement algorithms that alleviate tape mount time overhead and reduce ontape data fragmentation. Using 4.5 TB of realworld workloads, we show that DedupT retains at least 95 % of the deduplication efficiency. We show that DedupT mitigates major retrieval time overheads, and, due to reading less data, is able to offer better restore performance compared to the case of restoring nondeduplicated data. 1
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"... Abstract – Recent cryptanalytic attacks have exposed the vulnerabilities of some widely used cryptographic hash functions like MD5 and SHA1. Attacks in the line of differential attacks have been used to expose the weaknesses of several other hash functions like RIPEMD, HAVAL. In this paper we propo ..."
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Abstract – Recent cryptanalytic attacks have exposed the vulnerabilities of some widely used cryptographic hash functions like MD5 and SHA1. Attacks in the line of differential attacks have been used to expose the weaknesses of several other hash functions like RIPEMD, HAVAL. In this paper we propose a new efficient hash algorithm that provides a near random hash output and overcomes some of the earlier weaknesses. Extensive simulations and comparisons with some existing hash functions have been done to prove the effectiveness of the BSA, which is an acronym for the name of the 3 authors.