Showing papers by "Peter Wegner published in 1999"
TL;DR: 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 to motivate the use of interactive models as a basis for applications to computer architecture, software engineering, and artificial intelligence.
Abstract: 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.
45 citations
TL;DR: The role of coinductive methods in modeling finite interactive computing agents and the impact of interactive (coinductive) models on Church's thesis and the connection between incompleteness and greater expressiveness are examined.
36 citations
01 Sep 1999
TL;DR: The goal is to provide multiple perspective on interactive modeling from the viewpoint of interaction machines and mathematics, to persuade readers that interaction paradigms can play a significant role in narrowing the gap between theoretical models and software practice.
Abstract: D. Goldin, Univ. of Massachusetts - Boston P. Wegner, Brown University Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problem-solving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded systems are shown to be more expressive than algorithms. Multi-agent (distributed) models of coordination, collaboration, and true concurrency are shown to be more expressive than sequential models. The technology shift from algorithms to interaction is expressed by a mathematical paradigm shift that extends inductive definition and reasoning methods for finite agents to coinductive methods of set theory and algebra. An introduction to models of interactive computing is followed by an account of mathematical models of sequential interaction in terms of coinductive methods of non-well-founded set theory, coalgebras, and bisimulation. Models of distributed information flow and multi-agent interaction are developed, and the Turing test is extended to interactive sequential and distributed models of computation. Specification of interactive systems is defined in terms of observable behavior, Godel incompleteness is shown for interaction machines, and explanatory power of physical theories is shown to correspond to expressiveness for models of computation. Our goal is to provide multiple perspective on interactive modeling from the viewpoint of interaction machines and mathematics, to persuade readers that interaction paradigms can play a significant role in narrowing the gap between theoretical models and software practice.
25 citations
TL;DR: Interaction machines, which extend Turing Machines to interaction, are shown to be more expressive than Turing Machines by a direct proof, by adapting Godel's incompleteness result, and by observability metrics.
Abstract: Part I presents a model of interactive computation and a metric for expressiveness, Part II relates interactive models of computation to physics, and Part in considers empirical models from a philosophical perspective. Interaction machines, which extend Turing Machines to interaction, are shown in Part I to be more expressive than Turing Machines by a direct proof, by adapting Godel's incompleteness result, and by observability metrics. Observation equivalence provides a tool for measuring expressiveness according to which interactive systems are more expressive than algorithms. Refinement of function equivalence by observation of outer interactive behavior and inner computation steps is examined. The change of focus from algorithms specified by computable functions to interaction specified by observation equivalence captures the essence of empirical computer science.
23 citations
01 Sep 1999
TL;DR: The methods, formalisms, and tools for studying models of PTM computation developed in this paper can serve as a basis for a more comprehensive theory of interactive computation.
Abstract: D. Goldin, Univ. of Massachusetts - Boston P. Wegner, Brown University Persistent Turing machines (PTMs) are multitape machines with a persistent worktape preserved between successive interactions. They are a minimal extension of Turing machines (TMs) that express interactive behavior. Their behavior is characterized by input-output streams; PTM equivalence and expressiveness are defined relative to its behavior. Four different models of PTM behavior are examined: language-based, automaton-based, observation-based, and function-based. A number of special subclasses of PTMs are identified, and several expressiveness results are obtained, both for the general class of all PTMs and for the special subclasses. The methods, formalisms, and tools for studying models of PTM computation developed in this paper can serve as a basis for a more comprehensive theory of interactive computation.
11 citations