A method is provided for modifying an image. The method comprises displaying an image, the image comprising a portion of an object; and determining if an edge of the object is in a location within the portion. The method further comprises detecting movement, in a member direction, of an operating member with respect to the edge. The method still further comprises moving, if the edge is not in the location, the object in an object direction corresponding to the detected movement; and modifying, if the edge is in the location, the image in response to the detected movement, the modified image comprising the edge in the location.

Information processing apparatus, information processing method and program

A decision method for elementary algebra and geometry

A data storage and retrieval device and method is disclosed. The device includes at least one magnetic storage medium configured to store target data and at least one re-configurable logic device comprising an FPGA coupled to the at least one magnetic storage medium and configured to read a continuous stream of target data therefrom, having been configured with a template or as otherwise desired to fit the type of search and data being searched. The re-configurable logic device is configured to receive at least one search inquiry in the form of a data key and to determine a match between the data key and the target data as it is being read from the at least one magnetic storage medium. This device and method can perform a variety of searches on the target data including without limitation exact and approximate match searches, sequence match searches, image match searches and data reduction searches. This device and method may be provided as part of a stand-alone computer system, embodied in a network attached storage device, or can otherwise be provided as part of a computer LAN or WAN. In addition to performing search and data reduction operations, this device may also be used to perform a variety of other processing operations including encryption, decryption, compression, decompression, and combinations thereof.

Intelligent data storage and processing using fpga devices

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

/pdf/reachability-analysis-of-discrete-time-systems-with-4mpzsqbtkq.pdf

Reachability analysis of discrete-time systems with disturbances

Block ciphers encrypt blocks of plaintext, messages, into blocks of ciphertext under the action of a secret key, and the process of encryption is reversed by decryption which uses the same user-supplied key. Block ciphers are fundamental to modern cryptography, in fact they are the most widely used cryptographic primitive useful in their own right, and in the construction of other cryptographic mechanisms. In this book the authors provide a technically detailed, yet readable, account of the state of the art of block cipher analysis, design, and deployment. The authors first describe the most prominent block ciphers and give insights into their design. They then consider the role of the cryptanalyst, the adversary, and provide an overview of some of the most important cryptanalytic methods. The book will be of value to graduate and senior undergraduate students of cryptography and to professionals engaged in cryptographic design. An important feature of the presentation is the authors' exhaustive bibliography of the field, each chapter closing with comprehensive supporting notes.

The Block Cipher Companion

PROBLEM TO BE SOLVED: To improve security of a common key system relating to an expanded key generation device for generating an expanded key from a ciphered key by generating intermediate data from the ciphered key at a 1st step, selecting an arbitrary data from the intermediate data at a 2nd step to process it by a irreversible conversion and generating an expanded key of the arbitrary number of steps, and speedily generating expanded key of the arbitrary steps through the irreversible conversion. SOLUTION: This device is configured so as to be provided with an intermediate data generating means for dividing a bit string of an inputted cryptographic key into plural groups, generating an operation result of a plural number i by processing these divided groups of the bit strings each by arithmetic operation plural (i) times, performing an arithmetic operation for gathering the operation results together respectively among the plural groups concerning the operation results of the plural number i of each of these generated groups, and generating the plural number (i) of the intermediate data, and an expanded key generation for selecting one of the plural number (i) of the intermediate data based on the number of steps r of a specified expanded key, and processing the selected intermediate data by the irreversible conversion to generate the expanded key of the number of steps r.

Device and program for generating expanded key, and recording medium

PROBLEM TO BE SOLVED: To quickly obtain a proper solution even when a solution cannot be obtained within an allowable time by formula manipulationSOLUTION: An information processing method includes the steps of: generating a problem for a quantifier elimination method from a cost function representing a relation between a parameter set and a cost; causing a first module which executes processing for the quantifier elimination method with term substitution, to execute processing for the generated problem to obtain a first processing result; when the first processing result includes data of a partial problem not allowing the term substitution, causing a second module which executes numerical analysis processing, to perform processing of minimizing the cost for the partial problem not allowing the term substitution to obtain a second processing result; when the first processing result includes a logical expression being a solution of a partial problem subjected to the term substitution, generating first data for specifying a minimum cost value from the logical expression; and generating data representing a minimum cost for the problem from the second processing result and, if the first data has been generated, the first data

Information processing method, program, and apparatus

We introduce various aspects of design and implementation of a symbolic computation toolbox, called SyNRAC, handling first-order formulas on top of Maple. SyNRAC provides us with a new set of tools for solving real algebraic constraints derived from a broad range of applications in science and engineering.

SyNRAC: A Maple Toolbox for Solving Real Algebraic Constraints.

/pdf/development-of-synrac-a-cylindrical-algebraic-decomposition-55ycrfmosx.pdf

Development of SyNRAC : A Cylindrical Algebraic Decomposition Procedure (Computer Algebra : Design of Algorithms, Implementations and Applications)

We present SyNRAC, a symbolic computation package for solving real algebraic constraints. Algorithms in SyNRAC are implemented on the Maple software and they are expected to provide many users with symbolic methods of dealing with practical problems in engineering. SyNRAC is to be aimed to support symbolic, numerical, and symbolic-numeric computation. Until now we have emphasized on symbolic methods and implemented two types of special QE algorithms. Our project’s outline, the present state of SyNRAC, and our future plan are stated. 1 A Brief History of QE Quantifier elimination (QE) is a procedure that takes a first-order formula as input and returns a quantifier-free formula equivalent to the input. The history of QE dates back to the 1930s when Tarski proved the existence of a decision procedure for theory of real closed fields. Tarski also presented the first quantifier elimination algorithm, which was later modified by Seidenberg and is now known as the Seidenberg-Tarski algorithm [3, 10]. The algorithm requires too much computation, far from handling practical problems. In 1975 Collins [4, 5] achieved a historic breakthrough in QE. He provided a new decision method based on his concept of cylindrical algebraic decomposition (CAD). The complexity of the CAD algorithm is doubly exponential in the number of quantified variables, which greatly improved the Seidenberg-Tarski algorithm. Though Collins’s CAD method still could solve only very simple problems, it stimulated researchers to study this area. In the 1980s many revised algorithms and related research papers were presented. Some groups of people started implementing QE algorithms around 1990. The QEPCAD and ∗yanami@flab.fujitsu.co.jp †anai@jp.fujitsu.com c © 2003 Japan Society for Symbolic and Algebraic Computation J.JSSAC Vol. 10, No. 1, 2003 35 REDLOG packages have been known as pioneers and by far the famous ones; QE algorithms were also implemented on Mathematica and on Risa/Asir. For QEPCAD and REDLOG, see the respective articles in the present issue. Among the known general QE methods, the partial-CAD-based algorithm is known as the most organized and efficient one; the algorithm has been implemented in the QEPCAD package. In spite of the quality of the algorithm, its worst-case computation has still doubly exponential behavior. This fact promoted another point of view in studying QE and new approaches—QE algorithms that target only a certain type of formulas—were attempted in the 1990s. The method, known as the special QE method, enables us to make use of typical features of the prescribed formulas to reduce its computational complexity. With the help of these theoretical improvement as well as the year-by-year growth in hardware power such as CPU performance and memory size, various types of engineering problems can now be dealt with in reasonable time and space. 2 The SyNRAC Project We have been developing a toolbox including special QE methods on the Maple software. The toolbox has been named SyNRAC, which stands for a Symbolic-Numeric toolbox for Real Algebraic Constraints. The SyNRAC project started late last year after some successful results in solving practical engineering problems were obtained by using symbolic computation methods. The reasons why we have chosen Maple as a platform are: 1) Though Maple has been very popular among researchers in engineering, there are no QE tools available; 2) Maple provides us with a stable and friendly development environment; 3) Maple packages are automatically incorporated into MATLAB, which is widely used in engineering, via its “Symbolic Math Toolbox.” Based on SyNRAC we are planning to develop some toolboxes on MATLAB tailored for specific application fields such as robust control design. Those are expected to be novel tools and would provide engineers with new systematic design procedures using symbolic, numerical, and symbolic-numeric methods. 3 The Present State of SyNRAC It is just more than half a year since our SyNRAC project started. We are currently focusing on some known special QE algorithms, which are specialized to particular types of input formulas. Two sorts of special QE algorithms have been implemented so far and are now available in SyNRAC; one is a special QE algorithm for the sign definite condition (SDC) and the other is a special QE algorithm for linear formulas. These types of formulas 36 数式処理 第 10 巻 第 1 号 2003 cover a wide range of problems and the algorithms implemented have enough efficiency to solve various practical problems. These algorithms are each built around respective techniques. The former is based on the Sturm-Habicht sequence; the latter on virtual substitution. We briefly explain them in the next two subsections. Details of these algorithms are described in Anai and Yanami [2]. 3.1 Special QE Using the Sturm-Habicht Sequence The Sturm-Habicht sequence associated to a polynomial in R[x] is, in a word, a revised version of the well-known Sturm sequence. See [8] for the definition of the Sturm-Habicht sequence. The Sturm-Habicht sequence with respect to f(x) ∈ R[x] is a list of polynomials and is used for counting the number of real zeros of f in a given interval. The number of zeros of an interval, say, between a and b is calculated as follows: (1) Substitute a for x in the Sturm-Habicht sequence and count the number of sign changes over the resulting sequence; denote it by Na; (2) Do the same thing for the other endpoint b to obtain Nb; (3) The answer is the absolute value |Na −Nb| of the difference of these two numbers. Gonzalez-Vega [7] used the sequence to eliminate the quantifier in a first-order formula of the form ∀x, f(x) > 0, where f(x) ∈ R[x]. Anai and Hara [1] examined a similar type of formulas ∀x > 0, f(x) > 0 , and called this condition the sign definite condition (SDC). They also showed that a vast range of problems arising in engineering can be reduced to SDC and succeeded in solving them symbolically. It is easy to see that SDC is equivalent to the condition that f has no real zeros in the interval (0,+∞), plus f takes a positive value for some x > 0. By considering all the possible sign changes over the Sturm-Habicht sequence, we obtain an equivalent formula without the quantified variable x. 3.2 Special QE by Virtual Substitution The other QE algorithm implemented in SyNRAC deals with linear formulas by virtual substitution. A formula is called linear when every atomic subformula in it is linear with respect to its quantified variables, i.e., it is of the form a0 + a1x1 + · · ·+ anxn ρ 0 , where x1, ..., xn are the quantified variables, each term ai, 0 ≤ i ≤ n, contains no quantified variables, and ρ ∈ {=, 6=,≤, <}. In 1988 Weispfenning [11] proposed a QE algorithm by virtual substitution for linear formulas. The main idea for eliminating x in a formula ∃xφ(x) is to find a suitable finite J.JSSAC Vol. 10, No. 1, 2003 37 set of terms S = {a1, . . . , an} each term of which contains no x, so that the formula and φ(x//a1) ∨ · · · ∨ φ(x//an) are equivalent. Here φ(x//ai) is the formula obtained by a modified substitution. A theorem in [11] says that when the input is a linear formula, one can find S, called an elimination set, satisfying the above condition, and moreover, the resulting formula ∨s∈Sφ(x//s) is again linear. This fact, as well as the equivalence ∀xφ(x)⇐⇒¬(∃x¬φ(x)) with φ quantifier-free, enables us to eliminate all the quantifiers in a given linear formula; remove them one by one from inside. Loos and Weispfenning [9] have found elimination sets smaller than in [11], which promote to increase algorithm’s efficiency. We have implemented the algorithms in both papers.

Hitoshi Yanami

Papers

Device and program for generating expanded key, and recording medium

Information processing method, program, and apparatus

SyNRAC: A Maple Toolbox for Solving Real Algebraic Constraints.

Development of SyNRAC : A Cylindrical Algebraic Decomposition Procedure (Computer Algebra : Design of Algorithms, Implementations and Applications)

SyNRAC: A New Maple Package for Supporting Design and Analysis in Engineering (特集 Quantifier Elimination)