Takashi Horiyama

Finding Essential Attributes from Binary Data

We consider data sets that consist of n-dimensional binary vectors representing positive and negative examples for some (possibly unknown) phenomenon. A subset S of the attributes (or variables) of such a data set is called a support set if the positive and negative examples can be distinguished by using only the attributes in S. In this paper we study the problem of finding small support sets, a frequently arising task in various fields, including knowledge discovery, data mining, learning theory, logical analysis of data, etc. We study the distribution of support sets in randomly generated data, and discuss why finding small support sets is important. We propose several measures of separation (real valued set functions over the subsets of attributes), formulate optimization models for finding the smallest subsets maximizing these measures, and devise efficient heuristic algorithms to solve these (typically NP-hard) optimization problems. We prove that several of the proposed heuristics have a guaranteed constant approximation ratio, and we report on computational experience comparing these heuristics with some others from the literature both on randomly generated and on real world data sets.

Ordered binary decision diagrams as knowledge-bases

We consider the use of ordered binary decision diagrams (OBDDs) as a means of realizing knowledge-bases, and show that, from the view point of space requirement, the OBDD-based representation is more efficient and suitable in some cases, compared with the traditional CNF-based and/or model-based representations. We then present polynomial time algorithms for the two problems of testing whether a given OBDD represents a unate Boolean function, and of testing whether it represents a Horn function.

Folding of logic functions and its application to look up table compaction

The paper describes the folding method of logic functions to reduce the size of memories for keeping the functions. The folding is based on the relation of fractions of logic functions. We show that the fractions of the full adder function have the bit-wise NOT relation and the bit-wise OR relation, and that the memory size becomes half (8-bit). We propose a new 3--1 LUT with the folding mechanisms whcih can implement a full adder with one LUT. A fast carry propagation line is introduced for a multi-bit addition. The folding and fast carry propagation mechanisms are shown to be useful to implement other multi-bit operations and general 4 input functions without extra hardware resources. The paper shows the reduction of the area consumption when using our LUTs compared to the case using 4--1 LUTs on several benchmark circuits.

Speech recognition chip for monosyllables

In the paper, we present a real-time speech recognition chip for monosyllables such as A, B, ..., etc. The chip recognizes up to 64 monosyllables based on the Hidden Markov Model (HMM), which is a well known speaker-independent recognition method. The chip accepts a short-speech frame including 256 16-bit digitized samples corresponding to 11.6 msec period, and outputs the 6-bit symbol code of monosyllables for 16 short-frames (corresponding to 185.6 msec). A learning circuit to update HMM parameters for the recognition chip has also been designed, and the recognition chip includes an interface to the learning circuit. We have fabricated the recognition chip by VDEC Rohm 0.6 um process on a 4.5 mm x 4.5 mm chip. We have also made a layout of the entire circuit including the learning circuit by VDEC Rohm 0.35 um process on a 4.9 mm x 4.9 mm chip.

Reasoning with ordered binary decision diagrams

Abstract We consider problems of reasoning with a knowledge-base, which is represented by an ordered binary decision diagram, for two cases of general and Horn knowledge-bases. Our main results say that both finding a model of a knowledge-base and deducing from a knowledge-base can be done in linear time for a general knowledge-base, but that abduction is NP-complete even for a Horn knowledge-base. Then, we consider abduction when its assumption set consists of all propositional literals (i.e., an answer for a given query is allowed to include any positive literals), and show that it can be done in polynomial time if the knowledge-base is Horn, while it remains NP-complete for the general case. Some other solvable cases are also discussed.

Translation among CNFs, characteristic models and ordered binary decision diagrams

We consider translation among conjunctive normal forms (CNFs), characteristic models, and ordered binary decision diagrams (OBDDs) of Boolean functions. It is shown in this paper that Horn OBDDs can be translated into their Horn CNFs in polynomial time. As for the opposite direction, the problem can be solved in polynomial time if the ordering of variables in the resulting OBDD is specified as an input. In case that such ordering is not specified and the resulting OBDD must be of minimum size, its decision version becomes NP-complete. Similar results are also obtained for the translation in both directions between characteristic models and OBDDs. We emphasize here that the above results hold on any class of functions having a basis of polynomial size.

Translation among CNFs, Characteristic Models and Ordered Binary Decision Diagrams

We consider translation among conjunctive normal forms (CNFs), characteristic models, and ordered binary decision diagrams (OBDDs) of Boolean functions. It is shown in this paper that Horn OBDDs can be translated into their CNFs in polynomial time. As for the opposite direction, the problem can be solved in polynomial time if the ordering of variables in the resulting OBDD is speci.ed as an input. In case that such ordering is not specified and the resulting OBDD must be of minimum size, its decision version becomes NP-complete. Similar results are also obtained for the translation in both directions between characteristic models and OBDDs. We emphasize here that the above results holds on any class of functions having a basis B with B d.

A real-time 64-monosyllable recognition LSI with learning mechanism

In the paper, a real-time 64-mono-syllable recognition LSI is presented. The LSI accepts 11.6 msec speech frame and outputs a 6-bit symbol-code for each frame by the end of the next frame with the pipelining manner. The recognition method is based on the Hidden Markov Model and is speaker-independent. An on-chip learning mechanism has also been designed, but the circuit is off-chip at present implementation because of the restriction of LSI area. The LSI is fabricated by VDEC Rohm with 0.6 um process on a 4.5 mm x 4.5 mm chip.

Reasoning with Ordered Binary Decision Diagrams

We consider problems of reasoning with a knowledge-base, which is represented by an ordered binary decision diagram (OBDD), for two special cases of general and Horn knowledge-bases. Our main results say that both finding a model of a knowledge-base and deducing from a knowledge-base can be done in linear time for general case, but that abduction is NP-complete even if the knowledge-base is restricted to be Horn. Then, we consider the abduction when its assumption set consists of all propositional literals (i.e., an answer for a given query is allowed to include any positive literals), and show that it can be done in polynomial time if the knowledge-base is Horn, while it remains NP-complete for the general case. Some other solvable cases are also discussed.

Finding Essential Attributes in Binary Data

Given a data set, consisting of n-dimensional binary vectors of positive and negative examples, a subset S of the attributes is called a support set if the positive and negative examples can be distinguished by using only the attributes in S. In this paper we consider several selection criteria for evaluating the separation power of supports sets, and formulate combinatorial optimization problems for finding the best and smallest support sets with respect to such criteria. We provide efficient heuristics, some with a guaranteed performance rate, for the solution of these problems, analyze the distribution of small support sets in random examples, and present the results of some computational experiments with the proposed algorithms