This paper discusses some problems in Molecular Biology for which learning paradigms are strongly desired. We also present a framework of knowledge discovery by PAC-learning paradigm together with its theory and practice developed in our work for discovery from amino acid sequences.

Various authors have proposed probabilistic extensions of Valiant's PAC (Probably Approximately Correct) learning model in which the target to be learned is a (conditional) probability distribution. In this paper, we improve upon the best known upper bounds on the sample complexity of the parameter estimation part of the learning problem for distributions and stochastic rules over a finite domain with respect to the Kullback-Leibler divergence (KL-devergence). In particular, we improve the upper bound of order O(1/ε2) due to Abe, Takeuchi, and Warmuth to a bound of order O(1/ε). In obtaining our results, we made use of the properties of a specific estimator (slightly modified maximum likelihood estimator) with respect to the KL-divergence, while previously known upper bounds were obtained using the uniform convergence technique.

Complexity of Boolean functions satisfying the propagation criterion (PC), an extended notion of the perfect nonlinearity, is discussed on several computation models. The following topics are investigated: (i) relationships between the unateness and the degree of the PC, (ii) the inversion complexity of perfectly nonlinear Boolean functions, (iii) the formula size of Boolean functions that satisfy the PC of degree 1, (iv) the area-time-square complexity of VLSI circuits computing perfectly nonlinear Boolean functions, (v) the OBDD size perfectly nonlinear Boolean functions.

We define a new framework for rewriting graphs, called a formal graph system (FGS), which is a logic program having hypergraphs instead of terms in first-order logic. We first prove that a class of graphs is generated by a hyperedge replacement grammar if and only if it is defined by an FGS of a special form called a regular FGS. In the same way as logic programs, we can define a refutation tree for an FGS. The classes of TTSP graphs and outerplanar graphs are definable by regular FGSs. Then, we consider the problem of constructing a refutation tree of a graph for these FGSs. For the FGS defining TTSP graphs, we present a refutation tree algorithm of O(log2nlogm) time with O(nm) processors on an EREW PRAM. For the FGS defining outerplanar graphs, we show that the refutation tree problem can be solved in O(log2n) time with O(nm) processors on an EREW PRAM. Here, n and m are the numbers of vertices and edges of an input graph, respectively.

The analysis of the shielding properties of a planar wire-mesh shield embedded in a general isotropic--chirality is included--or anisotropic stratified media is here presented. A suitable model of the grating has been introduced in order to consider the occuring phenomena, in fact through a spectral technique the electromagnetic problem is translated into the equivalent circuit network model that allows to express the time response of the shielded field for the NEMP incidence in a closed form.

The wave forms of electric and magnetic fields radiated by short gap discharges are measured to analyze electrostatic discharge (ESD) events in the near-field zone with the monopole antennas, the loop antenna and the 5.5GHz bandwidth waveform digitizer. The antenna outputs are corrected by the measured characteristics of the antennas. The relations between the measured electric field and the discharge currents are discussed.

The analysis of the shielding properties of chiral materials slabs is here presented, first deriving the spectral representation of the shielded fields, then getting the asymptotic expression of the transmission matrix in the higher frequencies. The time response of the shielded field for the NEMP incidence is finally deduced in a closed form.

Graph unification is doubtlessly the most expensive process in unification-based grammar parsing since it takes the vast majority of the total parsing time of natural language sentences. A parsing time overload in unification consists in that, in general, no less than 60% of the graph unifications performed actually fail. Thus one way to achieve unification time speed-up is focusing on an efficient, fast way to deal with such unification failures. In this paper, a process, prior to unification itself, capable of filtering or stopping a considerably high percentage of graphs that would fail unification is proposed. This unification-filtering process consists of comparison of signatures that correspond to each one of the graphs to be unified. Unification-filter (hereafter UF) is capable of stopping around 87% of the non-unifiable graphs before unification itself takes place. UF takes significantly less time to detect graphs that do not unify and discard them than it would take to unification to fail the attempt to unify the same graphs. As a result of using UF, unification is performed in an around 71% of the time for the fastest known unification algorithm.

In this paper a method of recognizing waveform based on the Discrete Wavelet Transform (DWT) presented by us is applied to detecting the K-complex in human's EEG which is a slow wave overridden by fast rhythms (called as spindle). The features of K-complex are extracted in terms of three parameters: the local maxima of the wavelet transform modulus, average slope and the number of DWT coefficients in a wave. The 4th order B-spline wavelet is selected as the wavelet basis. Two channels at different resolutions are used to detect slow wave and sleep spindle contained in the K-complex. According to the principle of the minimum distance classification the classifiers are designed in order to decide the thresholds of recognition criteria. The EEG signal containing K-complexes elicited by sound stimuli is used as pattern to train the classifiers. Compared with traditional method of waveform recognition in time domain, this method has the advantage of automatically classifying duration ranks of various waves with different frequencies. Hence, it specially is suitable to recognition of signals which are the superimposition of waves with different frequencies. The experimental results of detection of K-complexes indicate that the method is effective.

A negation-limited circuit is a combinational circuit which includes at most [log(n1)] NOT gates. We show a relationship between the size of negation-limited circuits computing clique functions and the number of NOT gates in the circuits.

Two new algorithms for performing modular exponentiation are suggested. Nonstandard number systems are used. The first algorithm is based on the representing the exponent as a sum of generalized Fibonacci numbers. This representation is known as Zeckendorf representation. When precomputing is allowed the resulting algorithm is more efficient than the classical binary algorithm, but requires more memory. The second algorithm is based on a new number system, which is called hybrid binary-ternary number system (HBTNS). The properties of the HBTNS are investigated. With or without precomputing the resulting algorithm for modular exponentiation is superior to the classical binary algorithm. A conjecture is made that if more bases are used asymptotically optimal algorithm can be obtained. Comparisons are made and directions for future research are given.

We exactly determine the number of negations needed to compute the parity functions and the complement of the parity functions. We show that with k NOT gates, parity can be computed on at most 2k+11 variables, and parity complement on at most 2k+12 variables. The two bounds are shown to be tight.

For two finite disjoint sets P and Q of strings over an alphabet Σ, an alphabet indexing for P, Q by an indexing alphabet Γ with |Γ||Σ| is a mapping :ΣΓ satisfying (P)(Q), where :Σ*Γ* is the homomorphism derived from . We defined this notion through experiments of knowledge acquisition from amino acid sequences of proteins by learning algorithms. This paper analyzes the complexity of finding an alphabet indexing. We first show that the problem is NP-complete. Then we give a local search algorithm for this problem and show a result on PLS-completeness.

This paper presents a novel and successful logic synthesis method for optimizing ternary logic functions of any given number of input variables. A new optimization algorithm to synthesize and minimize an arbitrary ternary logic function of n-input variables can always lead this function to optimal or very close to optimal solution, where [n (n1)/2]1 searches are necessary to achieve the optimal solution. Therefore, the complexity number of this algorithm has been greatly reduced from O(3n) into O(n2). The advantages of this synthesis and optimization algorithm are: (1) Very easy logic synthesis method. (2) Algorithm complexity is O(n2). (3) Optimal solution can be obtained in very short time. (4) The method can solve the interconnection problems (interconnection delay) of VLSI and ULSI processors, where very fast and parallel operations can be achieved. A transformation method between operational and polynomial domains of ternary logic functions of n-input variables is also discussed. This transformation method is very effective and simple. Design of the circuits of GF(3) operators, addition and multiplication mod-3, have been proposed, where these circuits are composed of Josephson junction devices. The simulation results of these circuits and examples show the following advantages: very good performances, very low power consumption, and ultra high speed switching operation.

For a complex object model, a form of range restriction called specialization constraint (SC), has been proposed, which is associated not only with the properties themselves but also with property value paths. The domain and range of an SC, however, were limited to single classes. In this paper, SCs are generalized to have sets of classes as their domains and ranges. Let Σ be a set of SCs, where each SC in Σ has a set of classes as its domain and a non-empty set of classes as its range. It is proved that an SC is a logical consequence of Σ if and only if it is a finite logical consequence of Σ. Then a sound and complete axiomatization for SCs is presented. Finally, a polynomial-time algorithm is given, which decides whether or not an SC is a logical consequence of Σ.

We have made an exhaustive computation to establish that 33 comparisons never sort 13 items. The computation was carried out within 10 days by a workstation. Since merge insertion sort [Ford, et al. A tournament problem, Amer. Math. Monthly, vol. 66, (1959)] uses 34 comparisons for sorting 13 items, our result guarantees the optimality of the sorting procedure to sort 13 items as far as the number of comparisons is concerned. The problem has been open for nearly three decades since Mark Wells discovered that 30 comparisons are required to sort 12 items in 1965.

ACk is the class of problems solvable by an alternating Turing machine in space O(log n) and alternation depth O(logk n) [S. A. Cook, A taxonomy of problems with fast parallel algorithms, Inform. Contr. vol. 64]. We consider a game played by two persons: each player alternately moves a marker along an edge of a given digraph, and the first palyer who cannot move loses the game. It is shown that the problem to determine whether the first player can win the game on a digraph with n nodes exactly after logk n moves is complete for ACk nuder NC1 reducibility.

We define the complexity and the distortion-complexity of an individual finite length string from a finite set. Assuming that the string is produced by a stationary ergodic source, we prove that the distortion-complexity per source letter and its expectation approximate arbitrarily close the rate-distortion function of this source as the length of the string grows. Furthermore, we apply this property to construct a universal data compression scheme with distortion.

In computer vision, the interpretation of 3D motion of an object in the physical world is an important task. This study proposes a 3D motion interpretation method which uses a neural network system consisting of three kinds of neural networks. This system estimates the solutions of 3D motion of an object by interpreting three optical flow (OF-motion vector field calculated from images) patterns obtained at the different view points for the same object. In the system, OF normalization network is used to normalize diverse OF patterns into the normalized OF format. Then 2D motion interpretation network is used to interpret the normalized OF pattern and to obtain the object's projected motion onto an image plane. Finally, 3D motion interpretation network totally interprets the three sets of the projected motions and it derives the solutions of the object's 3D motion from the inputs. A complex numbered version of the back-propagation (Complex-BP) algorithm is applied to OF normalization netwerk and to 2D motion interpretation network, so that these networks can learn graphical patterns as complex numbers. Also a 3D vector version of the back-propagation (3DV-BP) algorithm is applied to 3D motion interpretation network so that the network can learn the spatial relationship between the object's 3D motion and the corresponding three OF patterns. Though the interpretation system is trained for only basic 3D motions consisting of a single motion component, the system can interpret unknown multiple 3D motions consisting of several motion components. The generalization capacity of the proposed system was confirmed using diverse test patterns. Also the robustness of the system to noise was probed experimentally. The experimental results showed that this method has suitable features for applying to real images.

There have been several interesting investigations on the space functions constructed by one-dimensional or two-dimensional Turing machines. On the other hand, as far as we know, there is no investigation about the space functions constructed by three-dimensional Turing machines. In this paper, we investigate about space constructibility by three-dimensional deterministic Turing machines with cubic inputs, and show that the functions log*n and log(k)n, k1, are fully space constructible by these machines.