Showing papers on "Hierarchy (mathematics) published in 1989"

The Boolean hierarchy II: applications

Abstract: The Boolean Hierarchy I: Structural Properties [J. Cai et al., SIAM J. Comput ., 17 (1988), pp. 1232–252] explores the structure of the boolean hierarchy, the closure of NP with respect to boolean ...

An Alternate Measure of Consistency

Abstract: The AΗΡ provides a decision maker with a way of examining the consistency of entries in a pairwise comparison matrix and the hierarchy as a whole through the consistency ratio measure. It has always seemed to us that this commonly-used measure could be improved upon. The purpose of this paper is to present an alternate measure of consistency and demonstrate how it might be applied. The contributions and limitations of the new measure are discussed.

A grammar-based approach towards unifying hierarchical data models

Abstract: A simple model for representing the hierarchical structure of information is proposed. This model, called the grammatical model, is based on trees that are generated by grammars; the grammars describe the hierarchy of the information represented by the trees. Two transformation languages, an algebra and a calculus, are presented and shown to be equally expressive.

Computer user interface with multimode selection of displayed controls

Abstract: A computer user interface includes a system and methods to provide a control hierarchy, control marking, a hybrid grammar, and resized and/or repositioned dialog boxes. Control hierarchy divides controls, assigns each control a label, displays the labels according to a design hierarchy, and operates on the controls according to a functional hierarchy. Control marking distinguishes controls, via addition of graphic elements or changes in labels--referred to as glyphs. Hybrid grammar simultaneously allows a user to specify operations and data objects in a noun verb relationship or verb noun relationship. Finally, resized and/or repositioned dialog boxes enable a user to select a control that requires selection of data objects that are possibly obscured by the dialog box.

A systematic approach to the soliton equations of a discrete eigenvalue problem

Abstract: The Ablowitz–Ladik (AL) problem is a linear vector difference equation whose isospectral flow equations include several important soliton equations; e.g., the discrete nonlinear Schrodinger equation: iqn=qn−1−2qn+qn+1 +‖qn‖2(qn−1+qn+1). There is an established procedure for describing the soliton hierarchy of the more familiar AKNS (Ablowitz, Kaup, Newell and Segur)problem. It is based on the notion of a generator for the hierarchy. In this paper the soliton equations of the AL hierarchy are described and characterized by a generator pair. A new continuous spectral problem is introduced and the AKNS hierarchy is embedded in its hierarchy as a specialization.

Expert system with knowledge base having term definition hierarchy

Abstract: A definition-based expert system and expert system shell. The expert system shell creates a knowledge base consisting of terms and their definitions, the definitions making up a hierarchy of definitions in which each definition depends only on terms defined at lower levels in the hierarchy or on term-independent values. Expert responses are obtained from the system by evaluating the terms. When a term is evaluated, all of the term-independent values and the values of all of the terms in its definition are obtained. The definitions include operators specifying operations which are to be performed when the defined term is evaluated. The operators include causing other systems operable in the digital computer system in which the expert system is operating to operate. The definitions further include table operators. Base table operators define terms representing tables and columns in the tables and permit loading of the tables. Query table operators define terms representing tables defined from base tables or other query tables. Column operators permit operations involving all of the fields of a column. The expert system is further able to respond to "don't know" values in a fashion which depends on the significance of the "don' t know" value for the definition of the term.

Games, equations and the dot-depth hierarchy

Abstract: This paper studies the fine structure of the Straubing hierarchy of star-free languages. The monoid varieties of some sublevels of level one of the hierarchy are shown to be characterized by certain natural equation systems. Those are then generalized to definitions of equation systems satisfied in monoid varieties of higher sublevels. A version of the Ehrenfeucht-Fraisse game is used to verify equations.

Wronskian determinants, the KP hierarchy and supersymmetric polynomials

Abstract: By using the Wronskian representation of the solutions of the bilinear KP hierarchy, a connection between Hirota derivatives and supersymmetric polynomials is brought to light. This correspondence is used in order to give an alternative construction of the hierarchy.

On the Power of Synchronization in Parallel Computations

Abstract: Hromkovi?, J., J. Karhumaki, B. Rovan and A. Slobodova, On the power of synchronization in parallel computations, Discrete Applied Mathematics 32 (1991) 155-182. This paper continues investigations of synchronized alternating machines which provide a natural model of communication of parallel processes. It is proved that synchronized alternating space SASPACE(S(n)) = Uc,e NSPACE(n . cScn)). Using this characterization of synchronized alternating space the following new characterizations of fundamental complexity classes are established: (1) UC>, DSPACE(cS’“‘) = uc>u ATIME( = uc>c SATIME(cS(“)) = SASPACE(S(n)) for S(n)?10g2n. (2) NSPACE(n) = 2(2SAFA), i.e. two-way synchronized alternating finite automata recognize exactly context-sensitive languages. (3) PSPACE = SALOGSPACE is exactly the class of languages recognized by two-way synchronized alternating multihead finite automata. Further, the parallel complexity of synchronized alternating finite automata is investigated and some hierarchy results are established. We also investigate the decidability problems for multihead and multitape automata from the new point of view. Instead of having one common finite state control enabling “full communication” of the heads as usual we consider k independent finite automata communicating only by synchronization. This represents a natural intermediate case between “full communication” and “no communication” and we present several new results and open problems for this form of communication of parallel processes. * This research was supported in part by the grant SPZV I-1-5/8. )166-218X/91/$03.50

Bounded query classes and the difference hierarchy

Abstract: LetA be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible toA based on bounding the number of queries toA that an oracle machine can make. WhenA is the halting problemK our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeoff between the number of parallel queries and the number of serial queries needed to compute a function with oracleK.

Probabilistic computation and linear time

Abstract: In this paper, we give an oracle under which BPP is equal to probabilistic linear time, an unusual collapse of a complexity time hierarchy. In addition, we also give oracles where DP2 is contained in probabilistic linear time and where BPP has linear sized circuits, as well as oracles for the negation of these questions. This indicates that these questions will not be solved by techniques that relativize. Finally, we note that probabilistic linear time can not contain both NP and BPP, implying that there are languages solvable by interactive proof systems that can not be solved in probabilistic linear time.

Object oriented programming in APL2

Abstract: In both the procedural and the non-procedural cases, the basic unit of execution is the program. The data only provide values that will be used to perform computations or to decide the order of execution. A given application is a hierarchical set of programs (modules) each of which is capable of invoking other programs in the hierarchy. The data may be global (accessible from every program in the hierarchy) or local (accessible by the program where they belong and, sometimes, by those at a lower level in the hierarchy).

Multi-level production scheduling for a class of flexible machining and assembly systems

Abstract: A class of machining and assembly systems characterised by a flat assembly component structure, the existence of families of similar items, non-negligible setups and fast material flow between work-centres is considered. A hierarchical production scheduling framework is proposed for this class of systems. The decision problems at each level of the hierarchy are identified and formulated. The formulations constitute a sufficiently accurate reflection of reality, while at the same time leading to tractable mathematical models that can be handled by carefully chosen and adapted optimisation techniques. The models can, when combined with suitable knowledge bases form the core of an effective multi-pass, hierarchical decision support system. Possible srategies for coordinating the various decision problems at the different levels of the hierarchy are also discussed.

The Use of Inverse Layout Trees for Hierarchical Design Rule Checking

Abstract: The inverse layout tree concept is used to perform fully hierarchical DRC without any constraints on the use of overlapping or incomplete cells that are completed at higher levels of hierarchy. Hierarchy is preserved and design rule violations are displayed in the cell where they should be corrected. The DRC is corner-based and processes 200-800 corners/second on a VAX 11/750.

Characterizing complexity classes by higher type primitive recursive definitions

Abstract: Higher type primitive recursive definitions (also known as Godel's system T) defining first-order functions can be classified into an infinite syntactic hierarchy. A definition is in the nth level of this hierarchy, a so-called rank-n definition, if and only if n is an upper bound on the levels of the types occurring in it. The author interprets these definitions over finite structures and shows that rank-2 definitions characterize PTIME, rank-3 definitions characterize PSPACE, and rank-4 definitions EXPTIME. >

Decidability, Recursive Enumerability and Kleene Hierarchy For L‐Subsets

Abstract: A constructive approach to fuzzy set theory requires an extension to fuzzy subsets of the basic notions of recursiveness theory such as the concept of decidability, recursive enumerability, computability and so on. The first steps in this direction have been made by E. T. LEE, L. A. ZADEH, E. S. SANTOS and other authors by the notions of fuzzy algorithm, fuzzy and probabilistic Turing machine, fuzzy program, fuzzy grammar and so on (see [7], [ll], [12], [13] and [IS]). A different approach is proposed in [l], [2] and [6] by the notions of decidability and recursive enumerability.

Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata

Abstract: An alternating auxiliary pushdown hierarchy is defined by extending the machine model of the Logarithmic Alternation Hierarchy by a pushdown store while keeping a polynomial time bound. Although recently it was proven by Borodin et al. that the class of languages accepted by nondeterministic logarithmic space bounded auxiliary pushdown automata with a polynomial time bound is closed under complement [Bo et al], it is shown that, surprisingly, the further levels of this alternating auxiliary pushdown hierarchy coincide level by level with the Polynomial Hierarchy. Furthermore, it is shown that PSPACE can be characterized by simultaneously logarithmic space and polynomial time bounded auxiliary pushdown automata with unbounded alternation.

Incorporation of information from the taxonomic hierarchy in comparing vegetation types

Abstract: Summary This paper reports on a method of extending species descriptions by incorporating information from the taxonomic hierarchy into a numerical classification of plant community types based on species. The basic species data are expanded to include information on higher taxonomic categories, such as genus, family, order, or class. Each stand is described by the presence, or abundance, of taxonomic categories but, unlike previous methods, only the necessary levels of the hierarchy are included. "Necessary" is here defined to be the highest level in the taxonomic hierarchy which uniquely identifies some specific taxon in the data set. If only a single member of an order is present in the data, then only taxonomic categories equal to or higher than, order are necessary to uniquely identify that taxon. Information on family, genus or species is simply redundant. Where several members of the same genus are present then all levels of the hierarchy will be recorded since they are all necessary for unique identification. Having obtained stand descriptions in terms of the taxonomic categories then classification can proceed normally using standard techniques. The method was applied to a small set of data, for which a variety of previous results was already available for comparison. The method appears to provide an effective means of extending species descriptions.

Design of an FMS operator workstation using the Rasmussen abstraction hierarchy

Abstract: A description is given of a research domain developed to study the role of human supervisory control in discrete manufacturing. A discussion is presented of the problems found when attempting to map J. Rasmussen's hierarchy (1986) directly to the discrete manufacturing domain. A methodology is proposed for extending Rasmussen's hierarchy to discrete manufacturing, and a plan to validate the hypothesis is suggested. >

Design of hierarchically distributed expert controllers for large-scale systems

Abstract: An architecture with expert distributed controllers to control large functional systems hierarchically is considered. A structural hierarchy was formed based on the physical structure of the system and functions associated with the structure. The hierarchy and the functional associations are described completely by the structural and functional coordinability axioms. These axioms display a very specific type of hierarchical structure. One of the properties of the hierarchy is that the whole system is represented both at the top and at the tip levels. It has the ability to represent the whole system at any desired detail. Moreover, representational redundancies are deliberately allowed, but the top and tip levels are forced to be represented without redundancies. The authors define the functional behavior of the system and the expert controller via six primitives. These primitives express the functions, capabilities, restrictions, and information to control the behavior of the system. Finally, the control process is described as a uniform flow from top to tip. >

Lower Bounds for the Low Hierarchy (Extended Abstract)

Abstract: The low hierarchy in NP [Sc-83] and the extended low hierarchy [BBS-86] have been useful in characterizing the complexity of certain interesting classes of sets. However, until now, there has been no way of judging whether or not a given lowness result is the best possible.

A solvable hierarchy of (n+1)-dimensional non-linear evolution-equations with constraints

Abstract: Matrix-multipolar asymptotic modules are used for introducing and solving a hierarchy of systems of purely differential non-linear equations. Each system consists of (N+1)-dimensional evolution equations and of quite strong differential constraints. Specific constructions of matrix-multipolar asymptotic modules are given, in particular delta constructions.

Object-Oriented Text Decomposition: A Methodology for Creating CAI Using Hypertext

Abstract: This paper presents a methodology for developing computer-assisted instructional material (CAI) intended for use in a transfer learning mode The development process is characterized by the ordered decomposition of an original knowledge base which will provide the information content of the tutorial The decomposition process keys on fleshing out key concepts and placing them into a hierarchy of levels of abstraction and detail, where relationships between concepts serve as links between levels In the process, the knowledge base is parsed into individual text passages, each essentially a mini-tutorial on a single concept-relationship pair The finished product is a formally structured collection of text passages

A new hierarchy of integrable systems and its hamiltonian structure

Abstract: On the basis of an analysis of the loop algebra ?_1 a new hierarchy of integrable sys-tems is proposed. The Hamiltonian structure of the new hierarchy of equations is established by means of constrained formal variational calculus. This hierarchy of evolution equations is demonstrated to possess an infinite number of conserved densities, which are ininvolution in pairs.

The organization of metastable states in a neural network with hierarchichal patterns

Abstract: We study the organization of the metastable states in a neural network where the memorized patterns are chosen according to a hierarchy. We find that the number of metastable states correlated with one of the stored patterns is dominated by states which exhibit the same hierarchy. It is argued that this property allows us to distinguish categories even when the stored patterns themselves are not retrieved well.