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 deened relative to its behavior. Four diierent models of PTM behavior are examined: language-based, automaton-based, function-based, and environment-based. A number of special subclasses of PTMs are identiied; several expressive-ness 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.