We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions.
A stream definition is called `productive' if it can be evaluated continually in such a way
that a uniquely determined stream in constructor normal form is obtained as the limit.
Whereas productivity is undecidable for stream definitions in general, we show that it can be decided for `pure' stream definitions.
For every pure stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements,
called `pebbles', in a finite `pebbleflow net(work)'.
And the production of a pebbleflow net associated with a pure stream definition, that is,
the amount of pebbles the net is able to produce at its output port, can be calculated by reducing nets to trivial nets.

See research for an overview of my research on productivity.

Bibtex

@inproceedings{productivity:streams:2007,
author = {Endrullis, J\"{o}rg and Grabmayer, Clemens and Hendriks, Dimitri and Isihara, Ariya and Klop, Jan Willem},
title = {{Productivity of Stream Definitions}},
booktitle = {Proc.\ Symp.\ on Fundamentals of Computation Theory (FCT~2007)},
number = {4639},
pages = {274--287},
publisher = {Springer},
series = {LNCS},
year = {2007},
doi = {10.1007/978-3-540-74240-1\_24},
keywords = {rewriting, infinitary rewriting, productivity},
type = {conference}
}