Iterated GSMs and Co-CFL

SummaryWe study the infinite words generated by an iterated gsm. The motivation was two fold. The first one was given by the apparent similarity between the iterated gsm and the iterated morphism. However contrary to the appearences almost all questions become undecidable. The second one was to disprove the following conjecture of Berstel: The language of coprefixes of an infinite word w is context free iff w is generated by an iterated gsm. We use for that the infinite word: w = abca2ba2bca4ba4ba2ba4bc ... (a2nb)2nc .... We prove also that the degree of the ambiguity problem for coprefixes of iterated gsm is Π1-complete in the Kleene hierarchy. This result fills the gap between the degree of this problem for iterated morphisms which is Π0 and for arbitrary context-free grammars which is Π2-complete.

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