In time alone: on the computational power of querying the history

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. In this paper we study the computational power of referring to the past primitive. To do that we propose a refined formal model, history dependent machine (RDM), 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, RDM can simulate any multicounter machine in real time. Then we show that the computations of RDM may be specified in the extension of propositional linear temporal logic by flexible constants, the abstraction operator and equality. We use then universality of RDM model to show that the above extension with a single flexible constant is not recursively axiomatizable