Coinductive counting with weighted automata

Authors:
J. J. M. M. Rutten
Affiliations:
CWI, P. O. Box 94079, NL-1090 GB Amsterdam, The Netherlands and Faculty of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081a, NL-1081 HV Amsterdam, The Netherlands
Venue:
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Year:
2003

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Abstract

A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute an expression (in terms of stream constants and operators) that represents the stream of all counts.