. 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 tool...

$-calculus is a higher-order polyadic process algebra for resource bounded computation. It has been designed to handle autonomous agents, evolutionary computing, neural nets, expert systems, machine learning, and distributed interactive AI systems, in general. $-calculus has built-in cost-optimization mechanism allowing to deal with nondeterminism, incomplete and uncertain information. In this paper, we investigate expressiveness of $-calculus. We show that due to innitary means, it allows to express models having richer behavior than Turing machine, including cellular automata, interaction machines, neural networks, and random automata networks. We also investigate the importance of synchronization, representation of continuity, and higher-order.

The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive computation due to the incompleteness of interaction. We show that interactive computation is necessarily paraconsistent, able to model both a fact and its negation, due to the role of the world (environment) in determining the course of the computation. We conclude that paraconsistency is a necessary property for a logic that can model interactive computation.

Genetic programming, autonomous agents, artif icial life and evolutionary computation share many common ideas. They generally investigate distributed complex processes, perhaps with the ability to interact. It seems to be natural to study their behavior using process algebras, which were designed to handle distributed interactive systems. $-calculus is a higher-order polyadic process algebra for resource bounded computation. It has been designed to handle autonomous agents, evolutionary computing, neural nets, expert systems, machine learning, and distributed interactive AI systems, in general. $-calculus has built-in cost-optimization mechanism allowing to deal with nondeterminism, incomplete and uncertain information. In this paper, we express in $-calculus several subareas of evolutionary computation, including genetic programming, artif icial life, autonomous agents and DNA-based computing. 1

Evolutionary computation in its essense represents a multi-agent competitive probabilistic search. It is useful for solutions of polynomial and hard optimization problems. The solutions found by evolutionary algorithms are not guaranteed to be optimal and evolutionary search is computationally very expensive. Using a generic $-calculus approach to AI, based on process algebras and anytime algorithms, we show that evolutionary search can be considered a special case of $-calculus k\Omega -search, and we present some results about completeness, optimality and search costs for evolutionary computation. The main result of the paper is to demonstrate how using $-calculus to make evolutionary computation totally optimal, i.e., how to allow to find the best quality solution with minimal search cost. 1

. 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. 1. Introduction Persistent Turing Machines (PTMs) are multitape machines with a persistent worktape preserved between successive interactions; they are a minimal extension o...

This paper presents a novel model for resource bounded computation based on process algebras.

Information systems design concern modeling systems that are dynamic in nature. A dynamic system essentially has two dimensions of concern -- static structure and dynamic behavior. The existence of dynamics -- or interactions among parts of the system distinguish a dynamic system from a heap or collection of parts. Specification and management of the static aspects of an information system like the data and metadata have been fairly well addressed by existing paradigms. However an understanding of the dynamic nature of information systems is still low. Currently most paradigms model behavioral properties above an existing structural model, resulting in what may be called "entity centric" modeling. Such a kind of modeling would neglect properties that can be attributed to behavioral processes themselves, and relationships that might exist among such processes. In this paper, we address behavioral modeling by first considering system behavior to be in the form of an abstract "interaction...

: This article formalizes the claim that interactive finite computing agents are more expressive than Turing machines. The impact of models of interaction on Church's thesis and Godel's incompleteness result is explored. The evolution from algorithmic to interactive models of computation in computer architecture, software engineering, and AI is considered in a final section. Contents 1. Interaction Machines 1.1. Sequential Interaction Machines (SIMs) 1.2. Interactive Behavior and Expressiveness 1.3. Multi-Stream Interaction Machines (MIMs) 2. Extensions of Expressiveness 2.1. Interactive Extensions of Machines, Sets, and Algebras 2.2. Interactive Extensions of the Church-Turing Thesis 3. Mathematical Models of Interaction 3.1. Non-Well-Founded Set Theory 3.2. Coalgebras 3.3. Beyond Non-Well-Founded Sets 4. From Induction to Coinduction 4.1. The Inductive Modeling Paradigm 4.2. Coinduction and Greatest Fixed Points 5. Metamathematics of Coinduction 5.1. From Formal Mode...

Information system (IS) design concerns different activities like conceptual modeling, database design, business process modeling and user modeling. However, despite the presence of an active research community that studies conceptual models for information systems, this term still lacks precise formal underpinnings. Unlike for databases, there is no agreement on what constitutes "principles of information systems." It would hence be desirable to provide formal underpinnings for information system design and to position it with respect to database design. At first glance, it is not clear that the principles underlining the study of information systems should be different than those for databases. Any significantly advanced IS incorporates some type of a database. As a consequence, information system design addresses a number of database issues like conceptual modeling of data elements, metadata management, etc. On the other hand, any useful database system is actually an info...