Generalized fairness and context-free languages

Kai Salomaa1, Sheng Yu2

Abstract

 The notion of fairness for generalized shuffle operations was introduced in []. The n-fairness property requires, roughly speaking, that in any prefix of a word the difference of the numbers of occurrences of two symbols is at most n. Here we give a new simplified proof for the decidability of uniform n-fairness for context-free languages. Also, we show that the more general, linear or logarithmic, fairness notions are decidable.

Footnotes:

  1 Department of Computer Science, University of Western Ontario, London, Ontario N6A 5B7, Canada, Email: ksalomaa,syu@csd.uwo.ca

  2 Research supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0041630.