Scope-Bounded Pushdown Languages

La Torre, Salvatore, Napoli, Margherita and Parlato, Gennaro (2016) Scope-Bounded Pushdown Languages International Journal of Foundations of Computer Science, 27, (2), pp. 215-233. (doi:10.1142/S0129054116400074).


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We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa). We show that scoped Mpa are indeed a robust model of computation, by focusing on the corresponding theory of visibly Mpa (Mvpa). We prove the equivalence of the deterministic and nondeterministic versions and show that scope-bounded computations of an n-stack Mvpa can be simulated, rearranging the input word, by using only one stack. These results have some interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and the effective semilinearity of the Parikh image (Parikh’s theorem). As a further contribution, we give a logical characterization and compare the expressiveness of the scope-bounded restriction with other Mvpa classes from the literature. To the best of our knowledge, scoped Mvpa languages form the largest class of formal languages accepted by Mpa that enjoys all the above nice properties.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1142/S0129054116400074
ISSNs: 0129-0541 (print)
Organisations: Electronic & Software Systems
ePrint ID: 386738
Date :
Date Event
5 December 2015Accepted/In Press
1 February 2016Published
Date Deposited: 30 Jan 2016 23:06
Last Modified: 17 Jun 2017 16:32
Further Information:Google Scholar

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