Borel Hierarchy and Omega Context Free Languages

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega context free languages : there exist some omega-CFL which are non Borel sets. And one cannot decide whether an omega-CFL is a Borel set. We give also an answer to questions of Niwinski and Simonnet about omega powers of finitary languages, giving an example of a finitary context free language L such that L^omega is not a Borel set. Then we prove some recursive analogues to preceding properties: in particular one cannot decide whether an omega-CFL is an arithmetical set.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Olivier Finkel. Borel Hierarchy and Omega Context Free Languages. Theoretical Computer Science, 2003, 290 (3), pp.1385-1405. ⟨hal-00103679v2⟩