The elementary formal system (EFS, for short) is a kind of logic program which directly manipulates character strings. This paper outlines in brief the authors' studies on algorithmic learning theory developed in the framework of EFS's. We define two important classes of EFS's and a new hierarchy of various language classes. Then we discuss EFS's as logic programs. We show that EFS's form a good framework for inductive inference of languages by presenting model inference system for EFS's in Shapiro's sense. Using the framework we also show that inductive inference from positive data and PAC-learning are both much more powerful than they have been believed. We illustrate an application of our theoretical results to Molecular Biology.

In this paper, we deal with inductive inference of an indexed family of recursive languages. We give two sufficient conditions for inductive inferability of an indexed family from positive data, each of which does not depend on the indexing of the family. We introduce two notions of finite cross property for a class of languages and a pair of finite tell-tales for a language. The former is a generalization of finite elasticity due to Wright and the latter consists of two finite sets of strings one of which is a finite tell-tale introduced by Angluin. The main theorem in this paper is that if any language of a class has a pair of finite tell-tales, then the class is inferable from positive data. Also, it is shown that any language of a class with finite cross property has a pair of finite tell-tales. Hence a class with finite cross property is inferable from positive data. Further-more, it is proved that a language has a finite tell-tale if and only if there does not exist any infinite cross sequence of languages contained in the language.

A pattern is a finite string of constant symbols and variable symbols. The language of a pattern is the set of all strings obtained by substituting any nonnull constant string for each variable symbol in the pattern. The class of pattern languages was introduced by Angluin in 1979 as a concrete class which is inferable from positive data. In this paper, we consider the decision problem whether for given two patterns there is a containment relation between their languages, which was posed by Angluin and its decidability remains open. We give some sufficient conditions to make this problem decidable. We also introduce the notions of generalizations and minimal generalizations common to a set of patterns. We characterize the above open problem using the minimal generalization.

In this paper, we consider the polynomial time inferability from positive data for unions of two tree pattern languages. A tree pattern is a structured pattern known as a term in logic programming, and a tree pattern language is the set of all ground instances of a tree pattern. We present a polynomial time algorithm to find a minimal union of two tree pattern languages containing given examples. Our algorithm can be considered as a natural extension of Plotkin's least generalization algorithm, which finds a minimal single tree pattern language. By using this algorithm, we can realize a consistent and conservative polynomial time inference machine that identifies unions of two tree pattern languages from positive data in the limit.

We consider the role of equivalence queries in learning unknown concepts using membership and equivalence queries. Equivalence queries have the following two roles: (R1) indicating whether a learning algorithm has succeeded to learn the unknown concept and (R2) providing counterexamples. In this paper, we consider the learning using membership and equivalence queries but using only the (R2) part of equivalence queries. In order to gain an insight into the learning membership and equivalence queries but using only the (R2) part of equivalence queries, we define equivalence-detecting problem". Let C be a representation class which is polynomial time learnable using membership and equivalence queries. We show that if the equivalence-detecting problem for C is polynomial time solvable then C is polynomial time learnable using membership and equivalence queries without using (R1). Moreover, we show that under certain conditions, the two notions, polynomial time solvability of equivalence-detecting problem" and polynomial time learnability using membership and equivalence queries without using (R1)", are equivalent. For concrete examples, we prove that dfas are polynomial time learnable using membership and equivalence queries without using (R1) in the learning situation where the algorithm is informed the number of states of the minimum states dfa accepting the target set in advance. On the other hand, we show that the equivalence-detecting problem for dfas are not solvable in the learning situation where the algorithm can use no additional information. This result together with our main result shows that, in this learning situation, the (R1) part of equivalence queries are necessary to learn dfas using membership and equivalence queries.

In the approximate learning model introduced by Valiant, it has been shown by Blumer et al. that an Occam algorithm is immediately a PAC-learning algorithm. An Occam algorithm is a polynomial time algorithm that produces, for any sequence of examples, a simple hypothesis consistent with the examples. So an Occam algorithm is thought of as a procedure that compresses information in the examples. Weakening the compressing ability of Occam algorithms, a notion of weak Occam algorithms is introduced and the relationship between weak Occam algorithms and PAC-learning algorithms is investigated. It is shown that although a weak Occam algorithm is immediately a (probably) consistent PAC-learning algorithm, the converse does not hold. On the other hand, we show how to construct a weak Occam algorithm from a PAC-learning algorithm under some natural conditions. This result implies the equivalence between the existence of a weak Occam algorithm and that of a PAC-learning algorithm. Since the weak Occam algorithms constructed from PAC-learning algorithms are deterministic, our result improves a result of Board and Pitt's that the existence of a PAC-learning algorithm is equivalent to that of a randomized Occam algorithm.

We investigate the relationship between two different notions of reducibility among prediction (learning) problems within the distribution-free learning model of Valiant (PAC learning model). The notions of reducibility we consider are the analogues for prediction problems of the many-one reducibility and of the Turing reducibility. The former is the notion of prediction preserving reducibility developed by Pitt and Warmuth, and its generalization. Concerning these two notions of reducibility, we show that there exist a pair of prediction problems A and B, whose membership problems are polynomial time solvable, such that A is reducible to B with respect to the Turing reducibility, but not with respect to the prediction preserving reducibility. We show this result by making use of the notion of a class of polynomially sparse variants of a concept representation class. We first show that any class A of polynomially sparse variants of another class B is reducible to B with respect to the Turing reducibility'. We then prove the existence of a prediction problem R and a class R of polynomially sparse variants of R, such that R does not reduce to R with respect to the prediction preserving reducibility.

This paper proposes a model for learning non-parametric densities using finite-dimensional parametric densities by applying Yamanishi's stochastic analogue of Valiant's probably approximately correct learning model to density estimation. The goal of our learning model is to find, with high probability, a good parametric approximation of the non-parametric target density with sample size and computation time polynomial in parameters of interest. We use a learning algorithm based on the minimum description length (MDL) principle and derive a new general upper bound on the rate of convergence of the MDL estimator to a true non-parametric density. On the basis of this result, we demonstrate polynomial-sample-size learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of exponential families with polynomial bases, and we prove that under some appropriate conditions, the sample complexity of learning them is bounded as O((1/ε)^(2r1)/2r1n^(2r1)/2r(1/ε)(1/ε)1n(1/δ) for a smoothness parameter r (a positive integer), where ε and δ are respectively accuracy and confidence parameters. Futher, we demonstrate polynomial-time learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of histogram densities with equal-length cells, and we prove that under some appropriate condition, the sample complexity of learning them is bounded as O((1/ε)^3/21n^3/2(1/ε)(1/ε)1n(1/δ)).

This paper presents a system that automatically refines the theory expressed in the function-free first-order logic. Our system can efficiently correct multiple faults in both the concept and subconcepts of the theory, given only the classified examples of the concept. It can refine larger classes of theory than existing systems can since it has overcome many of their limitations. Our system is based on a new combination of an inductive and an explanation-based learning algorithms, which we call the biggest-first multiple-example EBL (BM-EBL). From a learning perspective, our system is an improvement over the FOIL learning system in that our system can accept a theory as well as examples. An experiment shows that when our system is given a theory that has the classification error rate as high as 50%, it can still learn faster and with more accuracy than when it is not given any theory.

The meaning of analogical reasoning in locally stratified logic programs are described by generalized stable model (GSM) semantics. Although studies on the theoretical aspects of analogical reasoning have recently been on the increase, there have been few attempts to give declarative semantics for analogical reasoning. This paper takes notice of the fact that GSM semantics gives meaning to the effect that the negated predicates represent exceptional cases. We define predicates that denote unusual cases regarding analogical reasoning; for example, ab(x)p(x)g(x), where p(s), q(s), p(t) are given. We also add rules with negated occurrences of such predicates into the original program. In this way, analogical models for original programs are given in the form of GSMs of extended programs. A proof procedure for this semantics is presented. The main objective of this paper is not to construct a practical analogical reasoning system, but rather to present a framework for analyzing characteristics of analogical reasoning.

Syntax-directed editors have several advantages in editing programs because programming is guided by the syntax and free from syntax errors. Nevertheless, they are less popular than text editiors. One of the reason is that they force a priori specified editing structures on the user and do not allow him to use his own structure. ACE (Algorithmically Customizable syntax-directed Editor) provides a solution for this problem by using a technique of machine learning; ACE has a special function of customizing the grammar algorithmically and interactively based on the learning method for grammars from examples and queries. The grammar used in the editor is customized through interaction with the user so that the user can edit his program in a more familiar structure. The customizing function has been implemented based on the methods for learning of context-free grammars from structural examples, for which the correctness and the efficiency are proved formally. This guarantees the soundness and the efficiency of customization. Furthermore, ACE can be used as an algorithmic and interactive tool to design grammars, which is required for several purposes such as compiler design and pretty-printer design.

Parallel multiple context-free grammars (pmcfg's) and multiple context-free grammars (mcfg's) were introduced as extensions of context-free grammars to describe the syntax of natural languages. Pmcfg's and mcfg's deal with tuples of strings, and it has been shown that the universal recognition problem for mcfg's is EXP-POLY time-complete where the universal recognition problem is the problem to decide whether G generates w for a given grammar G and string w. In this paper, the universal recognition problems for the class of pmcfg's and for the subclass of pmcfg's with the information-lossless condition are shown to be EXP-POLY time-complete and PSPACE-complete, respectively. It is also shown that the problems for pmcfg's and for mcfg's with a bounded dimension are both -complete and those for pmcfg's and for mcfg's with a bounded degree are both -complete. As a corollary, the problem for modified head grammars introduced by Vijay-Shanker, et al. to define the syntax of natural languages is shown to be in deterministic polynomial time.

Lexical-Functional Grammars (LFG's) were introduced to define the syntax of natural languages. In LFG's, each node of a derivation tree has some attributes. An LFG G consists of a context-free grammar (cfg) G₀ called the underlying cfg of G and a description P_fs of constraints between the values of the attributes. P_fs can specify (1) constraints between the value of an attribute of a node and those of its children, and (2) constraints between the value of an attribute of a node called a controller and that of a node called its controllee. RLFG's were introduced as a subclass of LFG's. In RLFG's, only constraints between the value of an attribute of a node and those of its children can be specified. It is shown in this paper that the class of languages generated by RLFG's is equal to the class of recursively enumerable languages. Some restrictions on LFG's were proposed for the purpose of efficient parsing. Among them are (1) the condition called a valid derivation, and (2) the condition that the underlying cfg is cycle-free. For an RLFG G, if the production rules of the underlying cfg of G are of the form AaB or Aa for nonterminal symbols A, B and a terminal symbol a, then G is called an R-RLFG. Every R-RLFG satisfies the above restriction (1) and (2). It is also shown in this paper that the class of languages generated by R-RLFG's contains an NP-hard language, which means that parsing in deterministic polynomial time of LFG's is impossible in general (unless PNP) even if the above restrictions (1) and (2) are satisfied.

The main objective of this paper is to propose a new top-down subcube allocation scheme which has complete subcube recognition capability with quick response time. The proposed subcube allocation scheme, called Heuristic Subcube Allocation (HSA) strategy, is based on a heuristic and undirected graph, called Subcube (SC)-graph, whose vertices represent the free subcubes, and edge represents inter-relationships between free subcubes. It helps to reduce the response time and internal/external fragmentation. When a new subcube is released, the higher dimension subcube is generated by the cycle detection in the SC-graph, and the heuristic is used to reduce the allocation time and to maintain the dimension of the free subcube as high as possible. It is theoretically shown that the HSA strategy is not only statically optimal but also it has a complete subcube recognition capability in a dynamic environment. Extensive simulation results show that the HSA strategy improves the performance and significantly reduces the response time compared to the previously proposed schemes.

The effects of changing system parameters on job scheduling policies are studied for load balancing of multi-class jobs in a distributed computer system that consists of heterogeneous host computers connected by a single-channel communications network. A job scheduling policy decides which host should process the arriving jobs. We consider two job scheduling policies. The one is the overall optimal policy whereby jobs are scheduled so as to minimize the overall mean job response time. Tantawi and Towsley obtained the algorithm that gives the solution of the policy in the single class job environment and Kim and Kameda extended it to the multiple job class environment. The other is the individually optimal policy whereby jobs are scheduled so that every job may feel that its own expected response time is minimized. We can consider three important system parameters in a distributed computer system: the communication time of the network, the processing capacity of each node, and the job arrival rate of each node. We examine the effects of these three parameters on the two load balancing policies by numerical experiment.

Optimal static load balancing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. Their examples include optimal static load balancing in distributed computer systems and static routing in communication networks. We refer to the load balancing policy of minimizing the overall mean response (or sojourn) time of a job as the overall optimal policy. We show the conditions that the solutions of the overall optimal policy satisfy and show that the policy uniquely determines the utilization of each service center, the mean delay for each class and each path class, etc., although the solution, the utilization for each class, the mean delay for all classes at each service center, etc., may not be unique. Then we give tha linear relations that characterize the set whose elements are the optimal solutions, and discuss the condition wherein the overall optimal policy has a unique solution. In parametric analysis and numerical calculation of optimal values of performance variables we must ensure whether they can be uniquely determined.

In this paper, we present an automatic implementation method by which executable communication programs in C can be generated from protocol specifications in LOTOS. The implementation method consists of two parts: 1) An implementation strategy and 2) a set of translation rules. The first part consists of the basic ideas on how to realize the primary mechanisms in LOTOS specifications. The second part formulates the implementation method by way of the translation rules based on the implementation strategy. The characteristics of our method can be summarized as follows: We formulate our implementation method by way of translation rules. These rules are defined topdown in the form of syntax-directed translation function. The mechanism for controlling concurrency and communication among the user processes corresponding to the processes in LOTOS specification is easily realized by using UNIX operating system functions. The translation rules have been implemented on the AS 3000 (SUN3) workstation. An application of this implementation method is demonstrated by a simplified token-ring-protocol.

The numbers of passes required to realize permutations in the class of Bit Permute-Complement (BPC) permutations such as Bit-Reversal, Matrix-Transpose, Perfect-Shuffle, and Bit-Complement permutations in delta and extrastage delta networks are obtained. The influence of the faults in the networks on the number of passes required for them is also investigated. First, how different are the time complexities required when using a route decision algorithm and an improved algorithm having taken some inherent properties into consideration is discussed and solved by obtaining real data. Next, how many passes are required to realize BPC permutations in delta networks when faults are present and when not present, and how many passes can be reduced by using an extra-stage are discussed continuously. As an important criterion for the fault tolerance of multistage interconnecting networks, Dynamic Full Access (DFA) has been suggested. A weakness of DFA as applied to BPC permutations is that the ability to realize such permutations in a finite number of passes can not be always measured by a criterion of DFA, because of the uneven distributions of paths required for the permutations. This reason suggests the ability to realize such permutations must be investigated from the different angle.

The single fault model is invalid in many cases. However, it is very difficult to generate tests for all multiple faults since an m-line circuit may have 3^m --1 multiple faults. In this paper, we describe a method for generating tests for combinational circuits with multiple stuck-at faults. An input vector is a test for a fault on a target line, if it find the target line to be fault-free in the presence of undetected or undetectable lines. The test is called a robust test for fault on a target line. It is shown that the sensitizing input-pair for a completely single sensitized path can be a robust test-pair. The method described here consists of two procedures. We label these as SINGLE_SEN" procedure and DECISION" procedure. SINGLE_SEN generates a single sensitized path including a target line on it by using a PODEM-like method which uses a new seven-valued calculus. DECISION determines by utilizing the method proposed by H. Cox and J. Rajski whether the single sensitizing input-pair generated by the SINGLE_SEN is a robust test-pair. By using these two procedures the described method generates robust test-pairs for the combinational circuit with multiple stuck-at faults. Finally, we demonstrate by experimental results on the ISCAS85 benchmark circuits that SINGLE_SEN is effective for an algorithmic multiple fault test generation for circuits not including many XOR gates.

Logarithmic number systems (LNS) provide a very fast computational method. Their exceptional speed has been demonstrated in signal processing and then in computer graphics. But the precision problem of LNS in computer graphics has not been fully examined. In this paper analysis is made for the problem of LNS in picture generation, in particular for circle drawing. Theoretical error analysis is made for the circle drawing. That is, some expressions are developed for the relative error variances. Then they are examined by simulation experiments. Some comparisons are also done with floating point arithmetic with equivalent word length and dynamic range. The results show that the theory and the experiments agree reasonably well and that the logarithmic arithmetic is superior to or at least comparable to the corresponding floating point arithmetic with equivalent word length and dynamic range. Those results are also verified by visual inspections of actually drawn circles. It also shows that the conversion error (from integer to LNS), which is inherent in computer graphics with LNS, does not make too much influence on the total computational error for circle drawing. But it shows that the square-rooting makes the larger influence.

This paper deals with the problem of translating Japanese adnominal particles into English according to the idea of Example-Based Machine Translation (EBMT) proposed by Nagao. Japanese adnominal particles are important because: (1) they are frequent function words; (2) to translate them into English is difficult because their translations are diversified; (3) EBMT's effectiveness for adnominal particles suggests that EBMT is effective for other function words, e. g., prepositions of European languages. In EBMT, (1) a database which consists of examples (pairs of a source language expression and its target language translation) is prepared as knowledge for translation; (2) an example whose source expression is similar to the input phrase or sentence is retrieved from the example database; (3) by replacements of corresponding words in the target expression of the retrieved example, the translation is obtained. The similarity in EBMT is computed by the summation of the distance between words multiplied by the weight of each word. The authors' method differs from preceding research in two important points: (1) the authors utilize a general thesaurus to compute the distance between words; (2) the authors propose a weight which changes for every input. The feasibility of our approach has been proven through experiments concerning success rate.

A learning algorithm for neural controllers based on random search is proposed. The method presents an attractive feature in comparison with the learning of neural controllers using the standard backpropagation method. Namely, in this approach the identification of the unknown plant becomes unnecessary because the parameters of the controller are determined by a trial and error process. This is a favorable feature particularly in cases in which the characteristics of the system are complicated and consequently the identification is difficult or impossible to perform at all. As application examples, the learning control of the pendulum system and the maze problem are shown.

In general, a two-dimensional display is defined by two orthogonal unit vectors. In developing the display, discriminant analysis has a shortcoming that the extracted axes are not orthogonal in general. First, in order to overcome the shortcoming, we propose discriminant analysis which provides an orthonormal system in the transformed space. The transformation preserves the discriminatory ability in terms of the Fisher criterion. Second, we present a necessary and sufficient condition that discriminant analysis in the original space provides an orthonormal system. Finally, we investigate the relationship between orthogonal discriminant analysis and the Karhunen-Loeve expansion in the original space.