Scope-Bounded Pushdown Languages
Scope-Bounded Pushdown Languages
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.
215-233
La Torre, Salvatore
ec51ffc2-65d9-414e-9dd2-f5f342979c10
Napoli, Margherita
283e44c3-187a-4bdb-a582-79dbfe18aac8
Parlato, Gennaro
c28428a0-d3f3-4551-a4b5-b79e410f4923
1 February 2016
La Torre, Salvatore
ec51ffc2-65d9-414e-9dd2-f5f342979c10
Napoli, Margherita
283e44c3-187a-4bdb-a582-79dbfe18aac8
Parlato, Gennaro
c28428a0-d3f3-4551-a4b5-b79e410f4923
La Torre, Salvatore, Napoli, Margherita and Parlato, Gennaro
(2016)
Scope-Bounded Pushdown Languages.
International Journal of Foundations of Computer Science, 27 (2), .
(doi:10.1142/S0129054116400074).
Abstract
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.
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S0129054116400074 (1).pdf
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Accepted/In Press date: 5 December 2015
Published date: 1 February 2016
Organisations:
Electronic & Software Systems
Identifiers
Local EPrints ID: 386738
URI: http://eprints.soton.ac.uk/id/eprint/386738
ISSN: 0129-0541
PURE UUID: 6fd911b5-827d-4167-b2df-753e0c19ec1c
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Date deposited: 30 Jan 2016 23:06
Last modified: 14 Mar 2024 22:37
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Contributors
Author:
Salvatore La Torre
Author:
Margherita Napoli
Author:
Gennaro Parlato
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