Productivity of stream definitions

Authors:
Jörg Endrullis;Clemens Grabmayer;Dimitri Hendriks;Ariya Isihara;Jan Willem Klop
Affiliations:
Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam, The Netherlands;Universiteit Utrecht, Department of Philosophy, Utrecht, The Netherlands;Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam, The Netherlands;Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam, The Netherlands;Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam and Radboud Universiteit Nijmegen, Department of Computer Science, Nijmegen, The Netherlands
Venue:
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Year:
2007

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Abstract

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 continuously in such a way that a uniquely determined stream 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.