Dina Q. Goldin

On Similarity Queries for Time-Series Data: Constraint Specification and Implementation

Constraints are a natural mechanism for the specification of similarity queries on time-series data. However, to realize the expressive power of constraint programming in this context, one must provide the matching implementation technology for efficient indexing of very large data sets. In this paper, we formalize the intuitive notions of exact and approximate similarity between time-series patterns and data. Our definition of similarity extends the distance metric used in [2, 7] with invariance under a group of transformations. Our main observation is that the resulting, more expressive, set of constraint queries can be supported by a new indexing technique, which preserves all the desirable properties of the indexing scheme proposed in [2, 7].

Computation beyond turing machines

Seeking appropriate methods to model computing and human thought.

Turing’s Ideas and Models of Computation

The theory of computation that we have inherited from the 1960s focuses on algorithmic computation as embodied in the Turing Machine to the exclusion of other types of computation that Turing had considered. In this chapter we present new models of computation, inspired by Turing’s ideas, that are more appropriate for today’s interactive, networked, and embedded computing systems. These models represent super-Turing computation, going beyond Turing Machines and algorithms. We identify three principles underlying super-Turing computation (interaction with the world, infinity of resources, and evolution of systems) and apply these principles in our discussion of the implications of super-Turing computation for the future of computer science.

Constraint query algebras

Constraint query languages are natural extensions of relational database query languages. A framework for their declarative specification (constraint calculi) and efficient implementation (low data complexity and secondary storage indexing) was presented in Kanellakis et al., 1995. Constraint query algebras form a procedural language layer between high-level declarative calculi and low-level indexing methods. Just like the relational algebra, this intermediate layer can be very useful for program optimization. In this paper, we study properties of constraint query algebras, which we present through three concrete examples. The dense order constraint algebra illustrates how the appropriate canonical form can simplify expensive operations, such as projection, and facilitate interaction with updates. The monotone two-variable linear constraint algebra illustrates the concept of strongly polynomial operations. Finally, the lazy evaluation of (non)linear constraint algebras illustrates how large numbers of (non)linear constraints could be implemented with only a small amount of costly symbolic processing.

Persistent Turing Machines as a Model of Interactive Computation

Persistent Turing Machines (PTMs) are multitape machines with a persistent worktape preserved between interactions, whose inputs and outputs are dynamically generated streams of tokens (strings). They are a minimal extension of Turing Machines (TMs) that express interactive behavior. They provide a natural model for sequential interactive computation such as single-user databases and intelligent agents. PTM behavior is characterized observationally, by input-output streams; the notions of equivalence and expressiveness for PTMs are defined relative to its behavior. Four different models of PTM behavior are examined: language-based, automaton-based, function-based, and environment-based. A number of special subclasses of PTMs are identified; several expressiveness results are obtained, both for the general class of all PTMs and for the special subclasses, proving the conjecture in [We2] that interactive computing devices are more expressive than TMs. The methods and tools for formalizing PTM computation developed in this paper can serve as a basis for a more comprehensive theory of interactive computation.

Interaction as a Framework for Modeling

The irreducibility of interactive to algorithmic computing requires fundamental questions concerning models of computation to be reexamined. This paper reviews single-stream and multiple-stream interaction machines, extensions of set theory and algebra for models of sequential interaction, and interactive extensions of the Turing test. It motivates the use of interactive models as a basis for applications to computer architecture, software engineering, and artificial intelligence.

Variable independence and aggregation closure

We discuss the issue of adding aggregation to constraint databases. Previous work has shown that, in general, adding aggregates to constraint databases results in languages that are not closed. We show that by imposing a natural restriction, called variable independence (which is a generalization of the assumptions underlying the classical relational model of data) on the schema, we can guarantee that a restricted version of the language with aggregation is closed. We illustrate our approach irr the context of linear constraint databases.

The Interactive Nature of Computing: Refuting the Strong Church---Turing Thesis

The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new paradigm is hindered by the Strong Church–Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation more expressive than TMs are impossible. In this paper, we show that SCT reinterprets the original Church–Turing Thesis (CTT) in a way that Turing never intended; its commonly assumed equivalence to the original is a myth. We identify and analyze the historical reasons for the widespread belief in SCT. Only by accepting that it is false can we begin to adopt interaction as an alternative paradigm of computation. We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction. PTMs allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of TMs and of the CTT. The paradigm shift to interaction provides an alternative understanding of the nature of computing that better reflects the services provided by today’s computing technology.

Generating fuzzy semantic metadata describing spatial relations from images using the R-histogram

Automatic generation of semantic metadata describing spatial relations is highly desirable for image digital libraries. Relative spatial relations between objects in an image convey important information about the image. Because the perception of spatial relations is subjective, we propose a novel framework for automatic metadata generation based on fuzzy k-NN classification that generates fuzzy semantic metadata describing spatial relations between objects in an image. For each pair of objects of interest, the corresponding R-Histogram is computed and used as input for a set of fuzzy k-NN classifiers. The R-Histogram is a quantitative representation of spatial relations between two objects. The outputs of the classifiers are soft class labels for each of the following eight spatial relations: 1) LEFT OF, 2) RIGHT OF, 3) ABOVE, 4) BELOW, 5) NEAR, 6) FAR, 7) INSIDE, 8) OUTSIDE. Because the classifier-training stage involves annotating the training images manually, it is desirable to use as few training images as possible. To address this issue, we applied existing prototype selection techniques and also devised two new extensions. We evaluated the performance of different fuzzy k-NN algorithms and prototype selection algorithms empirically on both synthetic and real images. Preliminary experimental results show that our system is able to obtain good annotation accuracy (92%-98% on synthetic images and 82%-93% on real images) using only a small training set (4-5 images).

Coinductive Models of Finite Computing Agents

Abstract This paper explores the role of coinductive methods in modeling finite interactive computing agents. The computational extension of computing agents from algorithms to interaction parallels the mathematical extension of set theory and algebra from inductive to coinductive models. Maximal fixed points are shown to play a role in models of observation that parallels minimal fixed points in inductive mathematics. The impact of interactive (coinductive) models on Churchs thesis and the connection between incompleteness and greater expressiveness are examined. A final section shows that actual software systems are interactive rather than algorithmic. Coinductive models could become as important as inductive models for software technology as computer applications become increasingly interactive.