The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems

Jérôme Leroux (1) , Vincent Penelle (2) , Grégoire Sutre (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

Bounded languages have recently proved to be an important class of languages for the analysis of Turing-powerful models. For instance, bounded context-free languages are used to under-approximate the behav-iors of recursive programs. Ginsburg and Spanier have shown in 1966 that a bounded language L ⊆ a * 1 · · · a * d is context-free if, and only if, its Parikh image is a stratifiable semilinear set. However, the question whether a semilinear set is stratifiable, hereafter called the stratifiability problem, was left open, and remains so. In this paper, we give a partial answer to this problem. We focus on semilinear sets that are given as finite systems of linear inequalities, and we show that stratifiability is coNP-complete in this case. Then, we apply our techniques to the context-freeness problem for flat counter systems, that asks whether the trace language of a counter system intersected with a bounded regular language is context-free. As main result of the paper, we show that this problem is coNP-complete.

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

Jérôme Leroux, Vincent Penelle, Grégoire Sutre. The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems. ATVA'14, Nov 2014, Sydney, Australia. pp.248 - 263, ⟨10.1007/978-3-319-11936-6_19⟩. ⟨hal-01084819⟩