Bounded underapproximations

@article{Ganty2012BoundedU,
  title={Bounded underapproximations},
  author={Pierre Ganty and Rupak Majumdar and Benjamin Monmege},
  journal={Formal Methods in System Design},
  year={2012},
  volume={40},
  pages={206-231}
}
We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L′⊆L which has the same Parikh (commutative) image as L. Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form $w_{1}^{*}w_{2}^{*}\cdots w_{m}^{*}$ for some w1,…,wm∈Σ∗. In particular bounded context-free languages have nice structural and decidability properties. Our proof proceeds in two parts… 
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