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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01084819
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Submitted on : Thursday, November 20, 2014 - 10:50:18 AM
Last modification on : Saturday, June 25, 2022 - 10:35:23 AM
Long-term archiving on: : Friday, April 14, 2017 - 8:05:35 PM

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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⟩

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