Affiliations: Computer Science Department, University of Liverpool,
Ashton Building, Ashton Street, Liverpool, L69 3BX, UK. Lisitsa@liverpool.ac.uk;
Potapov@liverpool.ac.uk
Abstract: Querying its own history is an important mechanism in the
computations, especially those interacting with people or other computations
such as transaction processing, electronic data interchange. John McCarthy in
his Elephant programming language proposal suggested exploiting the referring
to the past as the main programming primitive. In this paper we study the
computational power of such primitive. In order to do that we propose a refined
formal model, History Dependent Machine (HDM), which uses querying the history
as its sole computational primitive. Our main result may be spelled in general
terms as: a model with a single agent wandering around a pool of resources and
having ability to check its own history for simple temporal properties has a
universal computational power. Moreover, HDM can simulate any multicounter
machine in real time. Then we show that the computations of HDM may be
specified in the extension of propositional linear temporal logic by flexible
constants, the abstraction operator and equality. We use then universality of
HDM model to show that the above extension with a single flexible constant is
not recursively axiomatizable.
Keywords: History-dependent computations, executable temporal logic, models of computations, universality
