-  Title
  
 -  On the Rigidity of a Vandermonde Matrix 
  
 -  Author(s)
  
 -  Tatsuie Tsukiji
  
 -  Contact person
  
 -  Tatsuie Tsukiji (tsukiji@cs.titech.ac.jp)             
  
 -  Abstract
  
 -  
 
  -  Title
  
 -  Analysis of a Japanese compound noun using collocatinal
       information
 
  
 -  Author(s)
  
 -  Kobayasi Yosiyuki
  
 -  Contact person
  
 -  Tokunaga Takenobu (take@cs.titech.ac.jp)
  
 -  Abstract
  
 -  This paper proposes a method to analyze the structure of compound
       nouns by using collocational information which are extracted from text
       and ordinary dictionaries.  The method has two parts: the part for
       analysis of the dependecy structure and the part for analysis of the
       syntactic relation.
 
  -  Title
  
 -  Integrating connection constraints into a GLR parser and its
       applications in a continuous speech recognition system
 
  
 -  Author(s)
  
 -  Hui Li
  
 -  Contact person
  
 -  Hozumi Tanaka tanaka@cs.titech.ac.jp
  
 -  Abstract
  
 -  This paper proposes a method to analyze the structure of compound
       nouns by using collocational information which are extracted from text
       and ordinary dictionaries.  The method has two parts: the part for
       analysis of the dependecy structure and the part for analysis of the
       syntactic relation.
       In this thesis, I propose a new method for integrating connection
       constraints into the GLR parsing algorithm.  I propose an algorithm
       for generating an LR table that combines both a grobal constraint and
       a local constraint.
 
  -  Title
  
 -  Optimal two-level unequal error control codes for computer
       systems
 
  
 -  Author(s)
  
 -  Tepparit Ritthongpitak, Masato Kitakami and Eiji Fujiwara
  
 -  Contact person
  
 -  Eiji Fujiwara (fujiwara@cs.titech.ac.jp)
  
 -  Abstract
  
 -  This paper proposes a method to analyze the structure of compound
       nouns by using collocational information which are extracted
       from text and ordinary dictionaries.  The method has two parts: the
       part for analysis of the dependecy structure and the part for analysis
       of the syntactic relation.  In this thesis, I propose a new method for
       integrating connection constraints into the GLR parsing algorithm.  I
       propose an algorithm for generating an LR table that combines both a
       grobal constraint and a local constraint.  Error control codes are now
       successfully applied to computer systems, especially to memory
       systems. This paper proposes an extended class of unequal error
       control codes which protects the fixed-byte strongly in computer words
       from multiple errors. The fixed-byte stores valuable information such
       as control and address information in computer/communication messages
       or pointer information in database words. Here, fixed-byte means the
       clustered information digits in the word whose position is determined
       in advance.  As a simple and practical class of the codes, this paper
       proposes an extended type of two-level unequal error control codes
       which has two error control levels in the codeword; one with strong
       error control function for the fixed-byte, and the other with weak
       function for the other part of the codeword. The proposed optimal
       codes are single-bit error correction, double-bit error detection and
       fixed b-bit byte error correction code, called SEC-DED-FbEC code, and
       single-bit plus fixed b-bit byte error correction code, called
       (S+Fb)EC code, which corrects single-bit errors and fixed-byte errors
       occurring simultaneously. For both types of codes, this paper
       clarifies necessary and sufficient conditions and bounds on code
       length, and demonstrates code construction method of the optimal codes
       and evaluation of these codes from the perspectives of error
       correction/detection capability and decoder hardware complexity.
 
  -  Title
  
 -  Admissibility of memorization learning with respect to
       projection learning in the presence of noise
 
  
 -  Author(s)
  
 -  Akira Hirabayashi and Hidemitsu Ogawa
  
 -  Contact person
  
 -  Akira Hirabayashi (hira@cs.titech.ac.jp)
  
 -  Abstract
  
 -  This paper proposes a method to analyze the structure of compound
       nouns by using collocational information which are extracted
       from text and ordinary dictionaries.  The method has two parts: the
       part for analysis of the dependecy structure and the part for analysis
       of the syntactic relation.  In this thesis, I propose a new method for
       integrating connection constraints into the GLR parsing algorithm.  I
       propose an algorithm for generating an LR table that combines both a
       grobal constraint and a local constraint.  Error control codes are now
       successfully applied to computer systems, especially to memory
       systems. This paper proposes an extended class of unequal error
       control codes which protects the fixed-byte strongly in computer words
       from multiple errors. The fixed-byte stores valuable information such
       as control and address information in computer/communication messages
       or pointer information in database words. Here, fixed-byte means the
       clustered information digits in the word whose position is determined
       in advance.  As a simple and practical class of the codes, this paper
       proposes an extended type of two-level unequal error control codes
       which has two error control levels in the codeword; one with strong
       error control function for the fixed-byte, and the other with weak
       function for the other part of the codeword. The proposed optimal
       codes are single-bit error correction, double-bit error detection and
       fixed b-bit byte error correction code, called SEC-DED-FbEC code, and
       single-bit plus fixed b-bit byte error correction code, called
       (S+Fb)EC code, which corrects single-bit errors and fixed-byte errors
       occurring simultaneously. For both types of codes, this paper
       clarifies necessary and sufficient conditions and bounds on code
       length, and demonstrates code construction method of the optimal codes
       and evaluation of these codes from the perspectives of error
       correction/detection capability and decoder hardware complexity.  In
       the training of multilayered feedforward neural networks using the
       error-backpropagation(BP) algorithm, it has been observed that
       the error over non-training set may increase, even though the error
       over training set decreases.  This phenomenon is referred to as
       over-learning.  In the previous works we showed how over-learning can
       be viewed as being the result of using the BP criterion as a
       substitute for some true criterion.  There, the concept of
       admissibility, which is defined using the relationship between the two
       criteria, was introduced.  In this paper we consider the case where
       the true criterion is the projection learning criterion, and give the
       necessary and sufficient conditions for the projection learning to
       admit memorization learning in the presence of noise. Based on these
       conditions, we devise a method of choosing the training sets so that
       the admissibility conditions are satisfied.
 
  -  Title
  
 -  A functional analytic approach to incremental learning in optimally generalizing neural networks
  
 -  Author(s)
  
 -  Sethu Vijayakumar and Hidemitsu Ogawa
  
 -  Contact person
  
 -  Sethu Vijayakumar (sethu@cs.titech.ac.jp)
  
 -  Abstract
  
 -  For a given set of training data, a method of learning for optimally
       generalizing neural networks using functional analytic approach already 
       exists. Here, we consider the case when additional training
       data is made available at a later stage. We devise a method of
       carrying out optimal learning with respect to the entire set of
       training data (including the newly added one) using the results
       of the previously learned stage. This ensures that the learning
       operator and the learned function can both be computed incrementally,
       leading to a reduced computational cost. Finally, we also provide a
       simplified relationship between the newly learned function and the
       previous function, opening avenues for work into selection of optimal
       training set.
 
  -  Title
  
 -  An improvement of the digital cash protocol of Okamoto and Ohta
  
 -  Author(s)
  
 -  Osamu Watanabe and Osamu Yamashita
  
 -  Contact person
  
 -  Osamu Watanabe (watanabe@cs.titech.ac.jp)
  
 -  Abstract
  
 -  Okamoto and Ohta proposed a digital cash protocol
       and showed that it satisfies some useful properties for digital
       cash as well as basic requirements such as security.  One of its
       features is ``divisibility''; i.e., a property that enable us to
       subdivide a piece of given digital cash into several pieces of smaller
       value.  This feature is made possible in Okamoto-Ohta protocol by
       using ``hierarchical structure table'', which is, intuitively, a
       collection of small coins.  That is, in Okamoto-Ohta protocol, one
       piece of digital cash is a collection of small coins, and a user can
       select some of them for his/her payment.  Then naturally, the amount
       of data transfer per payment may increase depending on the amount of
       the payment and how the coins have been used.  Here we propose a new
       protocol in which one digital cash can be regarded as a check book.
       That is, for each payment, a user can write a figure (within the
       limit) on one page of his/her digital check book, and pass it to a
       merchant.  Thus, in this protocol, we can fix the amount of data
       transfer per payment, which is much smaller than the average amount
       necessary in Okamoto-Ohta protocol.  For Okamoto-Ohta protocol, some
       cryptographic tools have been used, and for justifying them, we need
       some assumptions from computational complexity theory and
       computational cryptography such as the existence of public-key
       cryptosystems.  Our new protocol, which uses essentially the same
       cryptographic tools, is also based on such assumptions.
 
  -  Title
  
 -  NP-completeness results for NONOGRAM via parsimonious
       reductions
 
  
 -  Author(s)
  
 -  Nobuhisa Ueda and Tadaaki Nagao
  
 -  Contact person
  
 -  Nobuhisa Ueda (ueda@cs.titech.ac.jp)
  
 -  Abstract
  
 -  We introduce a new class of NP problems called ANOTHER SOLUTION
       PROBLEMs.  For a given NP problem X, ANOTHER SOLUTION PROBLEM
       for X (ASP for X) is to ask, for a given
       instance I for X and its solution, whether
       there is another solution for I.  The difficulty of
       ASP for X may not be immediate from the difficulty of 
       X.  For example, for some NP-complete problems such as
       3SAT or 3DM, 
       it is easy to show that their ASPs are NP-complete; on the other hand,
       ASP for, e.g., VERTEX COLORING is trivially in P.  In this paper, we
       propose one approach for showing the NP-completeness of ASP for a
       given NP problem X.  That is, for some NP problem
       Y for which it 
       is provable that ASP is NP-complete, we show a parsimonious reduction
       from Y to X that has the following additional
       property: given a 
       solution for an instance for Y, a solution for the
       corresponding 
       instance for X is computable in polynomial time.  Then the
       NP-completeness of ASP for Y clearly implies that of ASP for
       X.
       As an example of this approach, we demostrate the NP-completeness of
       ASP for one interesting puzzle ``NONOGRAM''.
 
  -  Title
  
 -  Partial Occam's razor and its applications
  
 -  Author(s)
  
 -  Carlos Domingo, Tatsuike Tsukiji and Osamu Watanabe
  
 -  Contact person
  
 -  Osamu Watanabe (watanabe@cs.titech.ac.jp)
  
 -  Abstract
  
 -  We introduce the notion of ``partial Occam algorithm''.
       A partial Occam algorithm produces a succinct hypothesis that
       is partially consistent with given examples, where the proportion of
       consistent examples is a bit more than half.  By using this new
       notion, we propose one approach for obtaining a PAC learning
       algorithm.  First, as shown in this paper, a partial Occam algorithm
       is equivalent to a weak PAC learning algorithm.  Then by using
       boosting techniques of Schapire or Freund, we can obtain an ordinary
       PAC learning algorithm from this weak PAC learning algorithm.  We
       demonstrate some examples that some improvement is possible by this
       approach.  First we obtain a new (non-proper) PAC learning algorithm
       for k-DNF, which has similar sample complexity as Littlestone's
       Winnow, but produces hypothesis of size polynomial in
       d and logk
       for a k-DNF target with n variables and
       d terms (Cf. The hypothesis size of Winnow is
       O(nk).  Next we show that 
       1-decision lists of length d with n variables
       are (non-proper) PAC learnable by using 
       O(1/epsilon (log 1/delta + 16d log n (d + log
       log n)2)) 
       examples within polynomial time w.r.t. n,
       2d, 1/epsilon, and
       log 1/delta.  Thus, for example, a class of decision lists of
       length O(log n) is polynomial time PAC learnable.
       
 
  -  Title
  
 -  The application of machine learning to student modeling: A
       survey and comparative analysis 
  
 -  Author(s)
  
 -  Raymund Sison  and Masamichi Shimura 
  
 -  Contact person
  
 -  Raymund Sison  (sison@cs.titech.ac.jp) 
  
 -  Abstract
  
 -  We first review and analyze using a common framework the various
       ways in which machine learning techniques have been used in student
       modeling, from LMS (Sleeman, 1982) to SMS1 (Sison and Reyes, 1995). 
       The major limitations of these works are the brute force style of
       inductive approaches to learning malrules and the relatively
       unintelligible malrules learned using the deductive application of
       perturbation rules. We then outline how two machine learning methods
       -- theory revision and conceptual clustering -- can be used to
       overcome these limitations.
 
  -  Title
  
 -  Incremental clustering of relational descriptions
  
 -  Author(s)
  
 -  Raymund Sison  and Masamichi Shimura 
  
 -  Contact person
  
 -  Raymund Sison  (sison@cs.titech.ac.jp) 
  
 -  Abstract
  
 -  We present an algorithm for the incremental clustering of relational
       descriptions. Major clustering algorithms in the literature can so
       far handle only attribute-value representations, though a few can
       handle ground relations. Preliminary results of applying the
       algorithm to the problem of bug interpretation in student modeling
       are presented and discussed.
 
  -  Title
  
 -  OSL language specification ver.2.0 (in Japanese)
  
 -  Author(s)
  
 -  Yasuhiro Iida
  
 -  Contact person
  
 -  Yasuhiro Iida (iida@cs.titech.ac.jp)
  
 -  Abstract
  
 -  This article defines the specification of OSL (ver.2.0).
       OSL is the description language of OOAG, which is
       a computational model based on attribute grammars
       extended with object-oriented features.
       The goal of OOAG is to describe and generate 
       language-based software databases.
       The rest part of the article is written in Japanese.
       New features from ver.1.0 are as follows:
       static type system, structured data types, 
       objects as data, revised remote object reference, 
       external class (interface to C++),
       attribution for attribute values,
       some restriction of message passing for efficiency,
       built-in infix operators.
 
  -  Title
  
 -  Constructing the campus network of Tokyo Institute of
       Technology
 
  
 -  Author(s)
  
 -  Yutaka Kikuchi
  
 -  Contact person
  
 -  Yutaka Kikuchi kikuchi@cs.titech.ac.jp
  
 -  Abstract
  
 -  The author turns out difficulties of volunteer based LAN management
       and provides some hints on proceeding it to business based management.
       First, the paper points out that a LAN would be faced with a
       fatal situation when it is managed by volunteers because of
       hidden difficulties.
       Second, the paper shows an experience in constructing a LAN of
       Tokyo Institute of Technology in early 1994. 
       The example provides some hints on proceeding to business based
       LAN management that is a solution of volunteer based one.
       The paper is a handout of the invited talk at JUS UNIX
       Symposium in August 1994.
 
 
  -  Title
  
 -  #P-completeness of counting graph edge colorings
  
 -  Author(s)
  
 -  Tadaaki Nagao
  
 -  Contact person
  
 -  Tadaaki Nagao (nagao@cs.titech.ac.jp)
  
 -  Abstract
  
 -  The problem of counting the number of edge-colorings of a graph
       is called #EDGE-COLORING.  While the associated decision problem was
       proved to be NP-complete, deciding whether a given graph is uniquely
       edge-colorable is known to be computable in polynomial time.  And it
       is known that if #EDGE-COLORING is reducible from #SAT via a
       reduction that preserves the number of solutions, then P = NP.  This
       aspect of #EDGE-COLORING is somewhat significant beside hundreds of
       known NP-complete problems.  In this paper, we prove that
       #EDGE-COLORING, however, still remains #P-complete.
 
  -  Title
  
 -  Simple yet effective algorithms for constraint satisfaction
       and related problems (doctoral thesis)
  
 -  Author(s)
  
 -  Hoong Chuin Lau
  
 -  Contact person
  
 -  Hoong Chuin Lau (hclau@cs.titech.ac.jp)
  
 -  Abstract
  
 -  In this thesis, we are mainly concerned with the design and
       analysis of simple yet provably effective algorithms to tackle various
       Constraint Satisfaction (CSP) and related problems.  The main topics
       of discussion are as follows.  We will study the computational
       complexity of and exact algorithms for restricted forms of the
       standard CSP.  We will consider random CSP instances and study the
       behavior of several types of local search algorithms. We show
       conditions under which local search performs well with high
       probability, both theoretically and experimentally. We next consider
       CSP optimization problems, namely, finding an assignment which
       maximizes certain linear objective functions.  For this, we will first
       propose and analyse the worst-case behavior of local search algorithms
       in finding approximate solutions. Next, we will propose and analyse a
       new approach based on the randomized rounding of mathematical
       programs.  Our theoretical results improve several known results in
       approximation of NP-hard problems.  In the final part of this thesis,
       we will present efficient algorithms to solve a special case of the
       CSP, the manpower scheduling problem, which has direct real-world
       applications.
 
  -  Title
  
 -  On data integration in software development environments
       based on object-oriented attribute grammars: OOAG
       (In Japanese)
 
  
 -  Author(s)
  
 -  Katsuhiko Gondow and Takuya Katayama
  
 -  Contact person
  
 -  Katsuhiko Gondow (gondow @cs.titech.ac.jp)
  
 -  Abstract
  
 -  We show the advantages and disadvantages of Object-Oriented Attribute
       Grammars (OOAG) when applying it to data modelling in software
       development environments (SDEs).  Attribute grammar approach for SDEs
       has many positive characteristics such as high readable and high
       maintainable description, high integration and fine granurarity due to
       abstract syntax tree, automatic generation of incremental attribute
       evaluator as change propagation engine.  But attribute grammars lack
       many object management issues like concurrency control, transactions,
       interactiveness.  OOAG has been introduced to solve these drawbacks of
       attribute grammars.  This paper shows the OOAG power of: (1) multiple
       subtree replacement by calculation, (2) remote object reference, as
       well as some problems that OOAG have not solved yet.  The rest part of
       this report is written in Japanese.
 
  -  Title
  
 -  Algorithms for learning finite automata from queries: a
       unified view
  
 -  Author(s)
  
 -  Jose José L. Balcázar, Josep Díaz,
       Ricard Gavald\`{a} and Osamu Watanabe
  
 -  Contact person
  
 -  Osamu Watanabe (watanabe@cs.titech.ac.jp)
  
 -  Abstract
  
 -  In this survey we compare several known variants of the 
       algorithm for learning deterministic finite automata via 
       membership and equivalence queries. We believe that our 
       presentation makes it easier to understand what is going 
       on and what the differences between the various algorithms 
       mean. We also include the comparative analysis of the 
       algorithms, review some known lower bounds, prove a new one, 
       and discuss the question of parallelizing this sort of
       algorithms.
       
 
  -  Title
  
 -  Coding complexity: the computational complexity of succinct
       descriptions
  
 -  Author(s)
  
 -  José L. Balcázar, Ricard Gavaldà and Osamu
       Watanabe
  
 -  Contact person
  
 -  Osamu Watanabe (watanabe@cs.titech.ac.jp)
  
 -  Abstract
  
 -  For a given set of strings,
       the problem of obtaining a succinct description
       becomes an important subject of research,
       related to several areas of theoretical computer science.
       In structural complexity theory,
       researchers have developed
       a reasonable framework for studying the complexity of these problems.
       In this paper,
       we survey how such investigation has proceeded,
       and explain the current status of our knowledge.
 
  -  Title
  
 -  A computational approach to the orientation selectivity
       problem I: a mathematical framework and some experimental
       results
  
 -  Author(s)
  
 -  Tadashi Yamazaki and Osamu Watanabe
  
 -  Contact person
  
 -  Osamu Watanabe (watanabe@cs.titech.ac.jp)
  
 -  Abstract
  
 -  Neurobiologists have found, in the primary visual cortex (area 17) of
       cat and monkey, some group of neurons that show ``orientation
       selectivity'', or ``orientation preference''.  That is, each of such
       neurons reacts strongly to the presentation of light bars of a certain
       orientation.  Furthermore, there is some evidence that such
       orientation selectivity is obtained in some animals through the
       training during the very early stage after the birth.  Neuroscientists
       have proposed several models explaining this process of developing
       orientation selectivity.  In fact, some of such models have been
       investigated mathematically.  Nevertheless, the problem has not been
       fully understood, and one can still look into it from different view
       points.  In this paper, we propose one mathematical framework, or a
       mathematical abstraction, on which we compare the behavior of several
       models for the selectivity.
 
  -  Title
  
 -  Reliable logic circuits with byte error control codes -- a
       feasibility study
  
 -  Author(s)
  
 -  Jien-Chung Lo, Masato Kitakami and Eiji Fujiwara
  
 -  Contact person
  
 -  Eiji Fujiwara (fujiwara@cs.titech.ac.jp)
  
 -  Abstract
  
 -  This paper addresses the relations between logic circuit synthesis, 
       error model and error control codes so that the efficient
       reliable logic circuits can be obtained. We propose that single fault
       masking capability of a random logic circuit can be obtained by
       encoding its outputs in a byte error correcting code; this is
       equivalent to that of the triple modulo redundancy (TMR)
       technique. Similarly, byte error detecting code can be used to provide
       an equivalence of duplication. In this paper, we address the problems
       and issues related to the realization of byte-organized configuration
       where the byte error control codes can be applied. Some MCNC benchmark
       circuits are used as examples to demonstrate the feasibility of the
       proposed concept.
 
  -  Title
  
 -  Metrics of error locating codes
  
 -  Author(s)
  
 -  Masato Kitakami, Shuxin Jiang and Eiji Fujiwara
  
 -  Contact person
  
 -  Eiji Fujiwara (fujiwara@cs.titech.ac.jp)
  
 -  Abstract
  
 -  Error locating codes were first presented by J. K. Wolf and B. Elspas
       in 1963. Recently, the error locating codes suitable for
       byte-organized semiconductor memory systems have been proposed. It is
       apparent that code conditions of error correcting/detecting codes are
       expressed by Hamming distance, but, on the other hand, those of error
       locating codes cannot always be expressed by only Hamming
       distance. That is, algebraic structure of the error locating codes has
       not yet been clarified.  This paper deduces the necessary and
       sufficient conditions of the error locating codes by using a newly
       defined metric and the function which represents the number of the
       bytes where Hamming distance between corresponding bytes of two
       codewords has a certain integer region. These conditions clarify the
       relation between the error locating codes and the error
       correcting/detecting codes. That is, the error locating code which can
       locate any byte errors is an error correcting code and if the byte
       length is equal to code length, an error locating code is an error
       detecting code.
       
 
  -  Title
  
 -  Concept formation in noisy domains
  
 -  Author(s)
  
 -  Xiaolong Zhang and Masayuki Numao
  
 -  Contact person
  
 -  Xiaolong Zhang (zxl@cs.titech.ac.jp)
  
 -  Abstract
  
 -  In inductive logic programming, concept formation in noisy domains 
       can be considered as learning from noisy data. This paper
       describes an approach to learning from noisy examples with an
       approximate theory. Although this kind of learning is more close to
       practical application, there are few systems can deal with such
       problems. The proposed learning approach includes a theory preference
       criterion and an overfitting avoidance technique. The theory
       preference criterion is a coding scheme which extends the minimum
       description length (MDL) principle principle by unifying model
       complexity and exception cost.  Model complexity is the encoding cost
       for an algorithm to obtain a logic program; exception cost is encoding
       length of the training examples misclassified by a theory.  By means
       of overfitting avoidance technique, the system learns more accurate
       clauses from the remainder of the training set after a revision
       session. Accounting for the above cases, our approach performs more
       accurately and efficiently compared with existing approaches.
       
 
  -  Title
  
 -  Probability to achieve TSC goal
  
 -  Author(s)
  
 -  Jien-Chung Lo and Eiji Fujiwara
  
 -  Contact person
  
 -  Eiji Fujiwara (fujiwara@cs.titech.ac.jp)
  
 -  Abstract
  
 -  In this paper we propose a probabilistic measure for self-checking (SC) 
       circuits that is analogous to reliability of fault-tolerant
       systems.  This measure is defined as the probability to achieve
       totally self-checking (TSC) goal at the t-th cycle: TSCG(t). TSCG
       provides insight to the worst case dynamic behavior of SC circuits
       with respect to the application environment and component failure
       rates. TSCG surpasses the TSC definitions in determining the
       applicability of a circuit in a given application environment. An SC
       circuit achieves TSC goal when no erroneous information or data is
       propagated beyond the boundary of this circuit. TSCG is therefore the
       probability that this fault confinement mechanism is intact.  The SC
       properties are obtained through adding hardware redundancy to the
       original design. Which means that an SC circuit has a higher failure
       rate than the original circuit. Further, there are tradeoffs between
       the level of hardware redundancy, the reliability, and the TSCG. We
       give several examples in this paper to clearly demonstrate these
       tradeoffs for different design environments. The proposed probability
       measure allows designers to choose from cost-effective SC designs that
       are suitable for their specifications.  We emphasize that the TSCG is
       intended to provide a mean of dynamic error handling performance
       evaluation of SC designs. The TSC definitions and alike are still
       intact, since a cost-effective SC circuit must begin with a TSC
       circuit. The TSCG gives confidence in the use of cost-effective error
       control codes and/or reduction in error handling capability. Analogous
       to reliability, the TSCG can be used in product specifications. This
       is a crucial step toward the practical applications of TSC or CED
       circuits.