Date: 09 Nov 2001

Persistent Turing Machines as a Model of Interactive Computation

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Abstract

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.