Showing papers on "Hierarchy (mathematics) published in 1993"

Materials with structural hierarchy

Abstract: The role of structural hierarchy in determining bulk material properties is examined. Dense hierarchical materials are discussed, including composites and polycrystals, polymers, and biological materials. Hierarchical cellular materials are considered, including cellular solids and the prediction of strength and stiffness in hierarchical cellular materials.

Types for dyadic interaction

Abstract: We formulate a typed formalism for concurrency where types denote freely composable structure of dyadic interaction in the symmetric scheme. The resulting calculus is a typed reconstruction of name passing process calculi. Systems with both the explicit and implicit typing disciplines, where types form a simple hierarchy of types, are presented, which are proved to be in accordance with each other. A typed variant of bisimilarity is formulated and it is shown that typed β-equality has a clean embedding in the bisimilarity. Name reference structure induced by the simple hierarchy of types is studied, which fully characterises the typable terms in the set of untyped terms. It turns out that the name reference structure results in the deadlock-free property for a subset of terms with a certain regular structure, showing behavioural significance of the simple type discipline.

Random-self-reducibility of complete sets

Abstract: This paper generalizes the previous formal definitions of random-self-reducibility. It is shown that, even under a very general definition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively random-self-reducible, unless the hierarchy collapses. In particular, NP-complete sets are not nonadaptively random-self-reducible, unless the hierarchy collapses at the third level. By contrast, we show that sets complete for the classes PP and ${\text{MOD}}_m {\text{P}}$ are random-self-reducible.

The Complexity of Set Constraints

Abstract: Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. We present several results on the computational complexity of solving systems of set constraints. The systems we study form a natural complexity hierarchy depending on the form of the constraint language.

Method and apparatus for providing a network configuration database

Abstract: A network database. The network database is arranged in a plurality of domains in a logical hierarchy. Each domain of the hierarchy represents a body of information associated with a logically related group of users or related group of computers. A relative naming scheme is implemented in which a domain stores the names of only its parent domain and child domains. This permits reconfiguration of the network to be accomplished without changing the database structure. Each domain stores information in a hierarchical structure known as a "directory." Each directory consists of a list of zero or more "properties," each having an associated name and ordered list of values.

Fixed-parameter tractability and completeness III: some structural aspects of the W hierarchy

Abstract: We analyse basic structural aspects of the reducibilities we use to describe xed parameter tractability and intractability, in the model we introduced in earlier papers in this series. Results include separation and density, the latter for the strongest reducibility.

Nimboran position class morphology

Abstract: The verbal morphemes in the Papuan language Nimboran are rigidly ordered; moreover, morphemes with identical ordering properties are in complementary distribution. This suggests that verbal morphemes belong to position classes, each permitting at most one member to surface. Certain morphemes belong simultaneously to more than one position class, with corresponding blocking of all morphemes in the relevant classes. A striking generalization is that position classes blocked in this joint fashion must be contiguous. The problem is that linear order and blocking diagnose two incompatible orderings for the position classes. The solution rests in reinterpreting verbalpositions as levels in a fixed morphological hierarchy; we resolve the ordering paradox by exploiting the distinction between dominance and precedence available in a hierarchical structure. This paper adduces new support for the theory of level-ordering and offers a formal theory of position class morphology, a well-known phenomenon which deserves attention in morphological theory. It also covers a large corpus of data — and certain phenomena — not previously discussed in the generative literature.

The Safety-Progress Classification

Abstract: We propose a classification of temporal properties into a hierarchy, called the safety-progress classification. The classes of the hierarchy are characterized through four views: a language-theoretic view, a topological view, a temporal logic view, and an automata view. In the topological view, the considered hierarchy coincides with the two lower levels of the Borel hierarchy, starting with the closed and open sets. For properties that are expressible by temporal logic and automata, we provide syntactic characterizations of the formulas and automata that correspond to properties in the different classes. We relate this classification to the well-known safety-liveness classification, and show that in some sense the two are orthogonal to one another.

Towards tractable algebras for bags

Abstract: Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the relationship between the depth of bag nesting and the expressive power, and (ii) the relationship between the algebraic operations, and their complexity and expressive power. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator.

Computer design system for mapping a logical hierarchy into a physical hierarchy

Abstract: A computer design system is used to map a logical hierarchy corresponding to the logical functions of an electronic system into a physical hierarchy corresponding to the physical positioning of the actual electronic components which will implement the logical functions of the system. The logical hierarchy contains several levels of logical entities connected by signals, and the physical hierarchy contains physical packages corresponding to electronic components, such as integrated circuits. The mapping is accomplished by designating partition group assertions (PGAs) for each of the logical entities in the logical hierarchy. Each PGA corresponds to one of the physical packages in the physical hierarchy. Each entity is grouped by common PGA designation, and each signal of each entity is classified as external, if the signal connects entities located on different physical packages, or internal, if the signal connects entities located on the same physical package. The physical hierarchy for the electronic system is generated using lists of these logical entity groupings and signal classifications. An advantage of the present invention is that partitioning of a logical design into a physical design is done automatically.

Hirota Bilinear Form for the Super-KdV Hierarchy

Abstract: The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form. We also conjecture a bilinear expression for the whole super-KdV hierarchy and check it to reasonably high orders. A by-product is an expression for the ordinary KdV hierarchy which provides an alternative to the ones obtained by Date et al. and Kac and Wakimoto.

An efficient way to learn English grapheme-to-phoneme rules automatically

Abstract: An efficient way to learn automatically grapheme-to-phoneme mapping rules for English by using Kohonen's concept of dynamically expanding context is presented. This method constructs rules that are most general in the sense of an explicitly defined specificity hierarchy. As the hierarchy, the amount of expanding context around the symbol to be transformed, weighted towards the right, is used. To apply this concept to English text-to-speech mapping, the authors have used the 20008-word corpus provided in the public domain by T. Sejnowski and C.R. Rosenberg (Complex Syst. vol.1, no.1, p.145-68 of 1987), which was also used in the NETTALK experiments. Phoneme-level mapping accuracies of 91% with data not used in training demonstrate that the dynamically expanding context is able to capture quite efficiently the context-dependent relationships in the corpus. >

Method for tree-structured hierarchical occlusion in image generators

Abstract: A method for determining which objects are visible in each pixel of a digitally-generated image is described. The method uses comparison of distances from the viewpoint (Z-sorting) for occlusion. The number of Z comparisons required is minimized by utilizing a hierarchy of regions in the screen area, and thereby, resolving occlusion for areas larger than pixel areas where possible. Use of the area hierarchy increases the efficiency of the occlusion processing. In a preferred implementation, the screen is divided into equal-sized horizontal regions each corresponding to typically four scanlines. Polygons for each image are subdivided into pieces that correspond to the preset hierarchy of regions, and occlusion processing occurs independently in parallel for two or more regions. Each region is subdivided further into smaller regions, each level of the hierarchy having regions half the size of a higher level region. The minimum and maximum Z values of a polygon's contribution to a region are compared to previously determined values for a hierarchy of subregions. Occlusion is accomplished at the highest level of the hierarchy at which portions of the incoming polygon contribution either occlude or are occluded by previous polygons. Provisions are made for transparent and interpenetrating polygons.

Some results on the dot-depth hierarchy

Abstract: In this paper we pursue the study of the decidability of the dot-depth hierarchy. We give an effective lower bound for the dotdepth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal'cev product. We also prove the equality of two decidable varieties which were known to contain all dot-depth two monoids. Finally, we restrict our attention to inverse monoids, and we prove that the class of inverse dot-depth two monoids is locally finite.

A methodology for formal expression of hierarchy in model solution

Abstract: A methodology for formal specification of hierarchy both in model specification and model solution is presented. Hierarchy is allowed to exist among different model types used in performance and dependability modeling. This offers a lot of flexibility and power to the modeler. The methodology presents a unified view of a variety of modeling techniques such as hierarchical composition, behavioral decomposition, iterative hierarchical modeling, reward-based performability modeling, aggregation, etc. This methodology brings the hierarchical modeling technique(s), based on which the model is constructed, to the fore. The results in a better understanding of the model by the user and it can simplify model validation if need be. Such a methodology would also make the design of modeling toolkits, which allow these modeling techniques, much simpler by presenting a conceptually simpler and unified view of a variety of modeling techniques. The formal expression is also expected to assist the modeler in construction of large, complex models. >

Reasoning with multiple abstraction models

Abstract: The problem of complexity has kept qualitative physics techniques from being applied to large real-world systems . Use of a hierarchy of abstract models is crucial for managing complexity . Several researchers have proposed ways to use an abstraction hierarchy of models to control the complexity of qualitative simulation [Falkenhainer & Forbus 88, Kuipers 87] . All the approaches proposed require models at pre-defined abstraction levels . Furthermore, the precise relations between different models are not explicitly defined, which makes it difficult to relate the conclusions drawn from different models to generate one coherent description of the behavior of the system as a whole . In this paper, we describe a scheme for generating models at abstraction levels appropriate for a given problem without requiring pre-defined set of abstract models. We also propose means for integrating behaviors produced from different abstraction models into one coherent description .

An incremental approach to reachability analysis of distributed programs

Abstract: In this paper we present an incremental approach to reachability analysis of distributed programs with synchronous communication and mailbox naming. Each process in a distributed program can be modeled as a communicating finite state machine (CFSM). A set of CFSMs is organized into a hierarchy. We present an algorithm that, for a given hierarchy of a set M of CFSMs, incrementally composes and reduces subsets of CFSMs in M. This incremental reachability analysis guarantees the detection of global deadlocks. We provide an algorithm for selecting a hierarchy for a set of CFSMs and show an incremental analysis of the gas station problem.

Pattern-based clustering for database attribute values

Abstract: We present a method for automatically clustering similar attribute values in a database system spanning mulitple domains. The method constructs an attribute abstraction hierarchy for each attribute using rules that are derived from the database instance. The rules have a confidence and popularity that combine to express the "usefullness" of the rule. Attribute values are clustered if they are used as the premise for rules with the same consequence. By iteratively applying the algorithm, a hierarchy of clusters can be found. The algorithm can be improved by allowing domain expert supervision during the clustering process. An example as well as experimental results from a large transportation database are included.

Counting, Selecting, adn Sorting by Query-Bounded Machines

Abstract: We study the query-complexity of counting, selecting, and sorting functions. That is, for a given set A and a positive integer k, we ask, how many queries to an arbitrary oracle does a polynomial-time machine on input (x1, x2,..., x k ) need to determine how many strings of the input are in A. We also ask how many queries are necessary to select a string in A from the input (x1, x2,..., x k ) if such a string exists and to sort the input (x1, x2,..., x k ) with respect to the ordering x ≼ y if and only if x ∈ A ⇒ y ∈ A. We obtain optimal query-bounds for these problems, and show that sets for which these functions have a low query-complexity must be easy in some sense. For such sets we obtain optimal placements in the extended low hierarchy. We also show that in the case of NP-complete sets the lower bounds for counting and selecting hold unless P=NP. Finally, we relate these notions to cheatability and p-superterseness. Our results yield as corollaries extensions of previously know results.

A hierarchical asynchronous replication protocol for large scale systems

Abstract: The authors present a new asynchronous replication protocol that is especially suitable for wide area and mobile systems, and allows reads and writes to occur at any replica. Updates reach other replicas using a propagation scheme based on nodes organized into a logical hierarchy. The hierarchical structure enables the scheme to scale well for thousands of replicas, while ensuring reliable delivery. A new service interface is proposed that provides different levels of asynchrony, allowing strong consistency and weak consistency to be integrated into the same framework. Further, the scheme provides the ability to offer different levels of staleness, depending upon the needs of various applications, by querying from different levels of the hierarchy. Also, it allows a selection from a number of reconciliation techniques based on delivery order mechanisms. Restructuring operations are provided to build and reconfigure the hierarchy dynamically without disturbing normal operation. The scheme tolerates transmission failures, node failures and network partitions.

Reflexive Reasoning with Multiple Instantiation in a Connectionist Reasoning System with a Type Hierarchy

Abstract: We describe a hybrid knowledge representation and reasoning system that integrates a rule-based reasoner with a type hierarchy and can accommodate multiple dynamic instantiations of predicates. The system—which is an extension of the reasoner described in Shastri and Ajjanagadde (1990)maintains and propagates variable bindings using temporally synchronous (i.e. in-phase)firing of appropriate nodes, and can perform a broad class of reasoning with extreme efficiency. The type hierarchy allows the system to encode generic facts such as ‘cats prey on bird’ and rules such as ‘if x preys on y then y is scared of ’ and use them to infer that Tweety the canary is scared of Sylvester the cat. The system can also encode qualified rules such as ‘if an animate agent collides with a solid object then the agent gets hur’. The ability to accommodate multiple dynamic instantiations of any predicate allows the system to handle a much broader class of inferences, including those involving transitivity and bounded ...

New symmetries of the Jaulent-Miodek hierarchy

Abstract: The inverse of the strong symmetry (recursion opterator) of Jaulent-Miodek hierarchy are expressed explicitly by means of the solutions of the Shrodinger equation. Four new sets of symmetries are obtained after acting the inverse strong symmetry on three new seed symmetryes and one known seed symmetry.

Equations and dot-depth one

Abstract: This paper studies the fine structure of the Straubing hierarchy of star-free languages. Sequences of equations are defined and are shown to be sufficiently strong to characterize completely the monoid varieties of a natural subhierarchy of level one. In a few cases, it is also shown that those sequences of equations are equivalent to finite ones. Extensions to a natural sublevel of level two are discussed.

Object-oriented viewing framework having view grouping

Abstract: A view system provides an extensible mechanism for associating a logical set of windows and manipulating them as a unit. For example, operations can be applied across address spaces to all the members of the group. A group is constructed by inserting a reference to each view in the group in a layer object. The layer object, in turn, can be inserted into a data hierarchy structure in a hierarchy object. The data hierarchy structure defines front to back display levels on a display and defines which windows overlap. Since all the members of the group are in the same layer object, they move to different levels as a group. Polymorphism and extensibility are provided via the object-oriented architecture of the operating system.

Non-locality in biological systems results from hierarchy. Application to the nervous system.

Abstract: The concept of non-locality is deduced from a new concept for biological systems, the “functional interaction”. It is shown that a biological system, which is expressed in terms of functional interactions, can be constructed as a hierarchical system, the dynamics of which are represented by a non-local field at each level of organization. The two following constraints: continuous representation of state variables and hierarchy of the system, result in non-locality, i.e., a space property according to which the system depends on mechanisms that are located elsewhere in the space. Concepts and theory are illustrated in the case of the nervous system, where two levels of organization are considered, the level of neurons and the level of synapses. Non-local versus local field operators are discussed, and an interpretation of the field equation terms is proposed. A general formulation of non-local operators for hierarchical systems is given.

Integrable hierarchy underlying topological Landau-Ginzburg models of D type

Abstract: A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-type is presented Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (‘positive’ and ‘negative’) sets of flows Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation This construction gives an embedding of the finite-dimensional small phase space of these models into the full space of flows of this hierarchy One of flat coordinates in the small phase space turns out to be identical to the first ‘negative’ time variable of the hierarchy, whereas the others belong to the ‘positive’ flows

Covariance structures for multidimensional data

Abstract: Certain covariance constraint sets useful in a wide class of signal processing problems are described. The constraint sets define structure in the covariance matrices of naturally multidimensional data organized into column-vector form. A notation characterizing these constraint sets is established. The structures involve a hierarchy of sub-blocks within the matrix, and include block-circulant and block-Toeplitz matrices and their respective generalizations. An example describing the structured covariance for wideband data from a uniform linear array of unstructured subarrays is included.