A family C of min-wise independent permutations is known to be a useful tool of indexing replicated documents on the Web. For any integer n>0, a family C of permutations on [n]={1,2,. . . ,n} is said to be min-wise independent if for any (nonempty) X [n] and any x X, Pr ( min {π(X)} = π(x))= ||X||-1 when π is chosen uniformly at random from C, where ||A|| is the cardinality of a finite set A. For any integer n>0, it has been known that (1) ||C|| lcm(n,n-1,. . . ,2,1) = en-o(n) for any family C of min-wise independent permutations on [n]; (2) there exists a polynomial time samplable C family of min-wise independent permutations on [n] such that ||C|| 4n. However, it has been unclear whether there exists a min-wise independent family C such that ||C|| = lcm(n,n-1,. . . ,2,1) for each integer n>0 and how to construct such a family C of min-wise independent permutations for each integer n>0 if it exists. In this paper, we shall construct a family Fn of permutations for each integer n>0 and show that Fn is min-wise independent and ||Fn|| = lcm(n,n-1,. . . ,2,1). Moreover, we present a polynomial time sampling algorithm for the family. Thus the family Fn of min-wise independent permutations is optimal in the sense of family size and is easy to implement because of its polynomial time samplability.

A min-wise independent permutation family is known to be an efficient tool to estimate similarity of documents. Toward good understanding of min-wise independence, we present a characterization of exactly min-wise independent permutation families by size uniformity, which represents certain symmetry of the string representation of a family. Also, we present a general construction strategy which produce any exactly min-wise independent permutation family using this characterization.

This paper demonstrates the slope isn't an appropriate parameter to characterize a signal regarding conducted electromagnetic disturbances. On the other hand, a relevant criterion is made conspicuous: it defines the maximum slope deviation between two segments forming a signal. This criterion is validated by a signal with a maximum slope of 400 mA/µs.

In this paper, a technique to reduce the overhead of Vector Quantization (VQ) coding is developed here. Our method exploits the inter-index correlation property to reduce the overhead to transmit encoded indices. Discrete Cosine Transform (DCT) is the tool to decorrelate the above correlation to get further bit rate reduction. As we know, the codewords in the codebook that generated from conventional LBG algorithm do not have any specified orders. Hence, the indices for selected codewords to represent respective adjacent blocks are random distributions. However, due to the homogeneous property existing among adjacent regions in original image, we re-arrange the codebook according to our predefined weighting criterion to enable the selected neighboring indices capable of indicating the homogeneous feature as well. Then, DCT is used to compress those VQ encoded indices. Because of the homogeneous characteristics existing among the selected adjacent indices after codebook permutation, DCT can achieve better compression efficiency. However, as we know, DCT introduces distortion by the quantization procedure, which yield error-decoded indices. Therefore, we utilize an index residue compensation method to make up that error decoded indices which have high complexity deviation to reduce those unpleasant visual effects caused by distorted indices. Statistics illustrators and table are addressed to demonstrate the efficient performance of proposed method. Experiments are carried out to Lena and other natural gray images to demonstrate our claims. Simulation results show that our method saves more than 50% bit rate to some images while preserving the same reconstructed image qualities as standard VQ coding scheme.

Feature interaction detection determines whether interactions occur or not between the new and existing telecommunication services. Most of conventional detection methods on state transition model utilize an exhaustive search. The exhaustive search is fundamentally very powerful in the sense that all interactions are exactly detected. However, it may suffer from the state explosion problem due to the exponential growth of the number of states in the model when the number of users and the number of features increase. In order to cope with this problem, we propose a new detection method using a state reduction technique. By means of a symmetric relation, called permutation symmetry, we succeed in reducing the size of the model while preserving the necessary information for the interaction detection. Experimental evaluation shows that, for practical interaction detection with three users, the proposed method achieves about 80% reduction in space and time, and is more scalable than the conventional ones especially for the increase of the number of users in the service.

Recently reported multidimensional geometrically uniform signal constellations (L MPSK and Decomposed-Lattice constellations) are joined in the term of Generalized Permutation Alphabets (GPA). Possibility of a binary isometric labeling of GPA's is completely characterized. An algorithm for constructing generating groups of PSK-type GPA is proposed. We show that this concept, when is extended to the lattice, gives rise to a class of new coset codes which perform out best codes listed in [11].

In this paper,we propose general fast one dimensional (1-D) and two dimensional (2-D) slant transform algorithms. By introducing simple and structural permutations, the heavily computational operations are centralized to become standardized and localized processing units. The total numbers of multiplications for the proposed fast 1-D and 2-D slant transforms are less than those of the existed methods. With advantages of convenient description in formulation and efficient computation for realization, the proposed fast slant transforms are suitable for applications in signal compression and pattern recognition.

For L 2, M 8, and transmission rate R = (log2M-1) bit/sym, a method for constructing GU trellis codes with L MPSK constellations is proposed and it is shown that the maximally achievable free distance is twice larger than it was previously reported for GU codes. Basides being geometrically uniform, these codes perform as good as Pietrobon's non-GU trellis codes with multidimensional MPSK constellations.

Weakness of a block cipher, which has provable immunity against linear cryptanalysis, is investigated. To this end, the round transformation used in MISTY, which is a data encryption algorithm recently proposed by M. Matsui from Mitsubishi Electric Corporation, is compared to the round transformation of DES from the point of view of pseudrandom generation. An important property of the MISTY cipher is that, in terms of theoretically provable resistance against linear and differential cryptanalysis, which are the most powerful cryptanalytic attacks known to date, it is more robust than the Data Encryption Standard or DES. This property can be attributed to the application of a new round transform in the MISTY cipher, which is obtained by changing the location of the basic round-function in a transform used in DES. Cryptograohic roles of the transform used in the MISTY cipher are the main focus of this paper. Our research reveals that when used for constructiong pseudorandom permutations, the transform employed by the MISTY cipher is inferior to the transform in DES, though the former is superior to the latter in terms of strength against linear and differential attacks. More specifically, we show that a 3-round (4-round, respectively) concatenation of transforms used in the MISTY cipher is not a pseudorandom (super pseudorandom, respectively) permutation.

Checkers, self-testers, and self-correctors for a function f are powerful tools in designing programs that compute f. However, the relationships among them have not been known well. In this paper, we first show that (1) if oneway permutations exist, then there exists a language L that has a checker but does not have a self-corrector. We then introduce a novel notion of "self-improvers" that trans form a faulty program into a less faulty program, and show that (2) if a function f has a self-tester/corrector pair, then f has a self-improver. As the applications of self-improvers, we finally show that (3) if a function f has a self-tester/corrector pair, then f has a flexible self-tester and (4) if a function f has a self-tester/corrector pair, then f has self-improver that transforms a faulty program into an alomost correct program.

A family of single-switch ZVS-CV (Zero-voltage switchingclamped voltage) dc-to-dc converters is presented. This class of converter is realized by employing a commutation inductor circuit which is connected in parallel with either the transistor or the freewheeling diode in a conventional PWM converter. The technique described here is simple and output-voltage control is easy. The converters that comprise this family are derived form Buck, Boost, Buck/Boost, Cuk, Sepic and Zeta PWM converters. The steady-state characteristics of these converters such as the voltage conversion ratio, the ZVS conditions, and the input and output current ripples are analyzed. The analysis is confirmed by experiment.

Polynomials are called permutation polynomials if they induce bijective functions. This paper investigates algebraic properties of permutation polynomials over a finite field, especially properties associated with permutation cycles. A permutation polynomial has a simple structure but good randomness properties suitable for applications. The cycle structure of permutations are considered to be related to randomness. We investigate the algebraic structure from the viewpoint of randomness. First we show the relationship between polynomials and permutations using a matrix equation. Then, we give a general form of a permutation polynomial corresponding to a product C1C2Ck of pairwise disjoint cycles. Finally, permutation polynomials with fixed points -or with 2, 3 and 4-cycles -and their compositions are given together with distribution of degree of the permutation polynomials.

Throughout the paper, the proper operating of the self-routing principle in 2-D shuffle multistage interconnection networks (MINs) is analysed. (The notation 1-D MIN and 2-D MIN is applied for a MIN which interconnects 1-D and 2-D data, respectively.) Two different methods for self-routing in 2-D shuffle MINs are presented: (1) The application of self-routing in 1-D MINs by a switch-pattern preserving transformation of 1-D shuffle stages into 2-D shuffle stages (and vice versa) and (2) the general concept of self-routing in 2-D shuffle MINs based on self-routing with regard to each coordinate which is the original contribution of the paper. Several examples are provided which make the various problems transparent.

A multiple instruction stream-multiple data stream (MIMD) computer is a parallel computer consisting of a large number of identical processing elements. The essential feature that distinguishes one MIMD computer family from another is the interconnection network. In this paper, we are concerned with a representative type of interconnection networks: the hypercube connected network. A family of regular graphs is presented as a possible candidate for the implementation of a distributed system and for fault-tolerant architectures. The symmetry of graphs makes it possible to determine message routing by using a simple distributed algorithm. A candidate having the same property is the hypercube connected network. Arbitrary data permutations are generally accomplished by sorting. For certain classes of permutations, however, this is, for many frequently used permutations in parallel processing such as bit reversal, bit shuffle, bit complement, matrix transpose, butterfly permutations used in FFT algorithms, and segment shuffles, there exist algorithms that are more efficient than the best sorting algorithm. One such class is the bit permute complement (BPC) class of permutations. In this paper, we, first, develop an algorithm to realize an arbitrary BPC permutation in hypercube connected networks. The developed algorithm in hypercube connected networks requires only 1 token memory register in each node. We next evaluate the ability to realize BPC permutations in these networks of an arbitrary size by estimating the number of required routing steps.

A permutation cipher scheme using polynomials over a field is presented. A permutation as well as substitution plays a major role in almost all conventional cryptosystems. But the security of the permutation depends on how symbols are permuted. This paper proposes the use of polynomials for the permutation and show that the scheme satisfies the following security criteria. (1) There are enough encryption keys to defend exhaustive attacks. (2) The permutation moves almost all samples into places which are different from the original places. (3) Most samples are shifted differently by different permutations. The permutation cipher scheme could be regarded as a scheme based on Reed-Solomon codes. The information symbols of the codes compose a key of the permutation cipher scheme.

Damgrd defined the notion of a collision intractable hash functions and showed that there exists a collection of collision intractable hash functions if there exists a collection of claw-free permutation pairs. For a long time, the necessary and sufficient condition for the existence of a collection of collision intractable hash functions has not been known, however, very recently Russell finally showed that there exists a collection of collision intractable hash functions iff there exists a collection of claw-free pseudo-permutation pairs. In this paper, we show an alternative necessary and sufficient condition for the existence of a collection of collision intractable hash functions, i.e., there exists a collection of collision intractable hash functions iff there exists a collection of distinction intractable pseudo-permutations.

A multiple instruction stream-multiple data stream (MIMD) computer is a parallel computer consisting of a large number of identical processing elements. The essential feature that distinguishes one MIMD computer family from another is the interconnection network. In this paper, 2 representative types of interconnection networks are dealt with the chordal ring network and the mesh connected network. A family of regular graphs of degree 3, called chordal rings is presented as a possible candidate for the implementation of a distributed system and for fault-tolerant architectures. The symmetry of graphs makes it possible to determine message routing by using a simple distributed algorithm. Another candidate having the same property is the mesh connected networks. Arbitrary data permutations are generally accomplished by sorting. For certain classes of permutations, however, there exist algorithms that are more efficient than the best sorting algorithm. One such class is the bit permute complement (BPC) class of permutations. The class of BPC permutations includes many of the frequently occurring permutations such as bit reversal, bit shuffle, bit complement, matrix transpose, etc. In this paper, we evaluate the abilities of the above networks to realize BPC permutations. In this paper, we, first, develop algorithms required 2 token storage registers in each node to realize an arbitrary BPC permutaion in both chordal ring networks and mesh connected networks. We next evaluate the ability to realize BPC permutations in these networks of an arbitrary size by estimating the number of required routing steps.

In this paper we estimate the number of permutations realizable in fault-tolerant multistage interconnection networks designed to tolerate faults on any switching element. The Parallel Omega network and the INDRA network are representative types of fault-tolerate multistage interconnection networks designed to tolerate a single fault. In order to evaluate the enhancement in the function of network by preparing the hardware redundancy for fault-tolerance, we estimate the number of permutations realizable in fault-tolerant networks. This result enables us to set up a standard to evaluate the hardware redundancy required to tolerate multifaults from the viewpoint of the enhancement of network function. This paper concludes that in the case where the number of inputs is up to 32 the increase ratio of the number of realizable permutations is no more than 1/0.73 even if the tolerance to multifaults is prepared instead of the tolerance to a single fault.

Binary decision diagrams (BDD's) are graph representations of Boolean functions, and at the same time they can be regarded as a computational model. In this paper, we discuss relations between BDD's and other computational models and clarify the computational power of BDD's. BDD's have the property that each variable is examined only once according to a total order of the variables. We characterize families of BDD's by on-line deterministic Turing machines and families of permutations. To clarify the computational power of BDD's, we discuss the difference of the computational power with respect to the way of reading inputs. We also show that the language TADGAP (Topologically Arranged Deterministic Graph Accessibility Problem) is simultaneously complete for both of the class U-PolyBDD of languages accepted by uniform families of polynomial-size BDD's and the clas DL of languages accepted by log-space bounded deterministic Turing machines. From the results, we can see that the problem whether U-PolyBDD U-NC1 is equivalent to a famous open problem whether DL U-NC1, where U-NC1 is the class of languages accepted by uniform families of log-depth constant fan-in logic circuits.

An idea of optimal output permutation of multiple-valued sum-of-products expressions is presented. The sum-of-products involve the TSUM operator on the MIN of window literal functions. Some bounds on the maximum number of implicants needed to cover an output permuted function are clarified. One-variable output permuted functions require at most p1 implicants in their minimal sum-of-products expressions, where p is the radix. Two-variable functions with radix between three and six are analyzed. Some speculations of maximum number of the implicants could be established for functions with higher radix and more than 2-variables. The result of computer simulation shows that we can have a saving of approximately 15% on the average using permuting output values. Moreover, we demonstrate the output permutation based on the output density as a simpler method. For the permutation, some speculation is shown and the computer simulation shows a saving of approximately 10% on the average.