Two-Way Parikh Automata with a Visibly Pushdown Stack

Abstract : In this paper, we investigate the complexity of the emptiness problem for Parikh automata equipped with a pushdown stack. Push-down Parikh automata extend pushdown automata with counters which can only be incremented and an acceptance condition given as a semi-linear set, which we represent as an existential Presburger formula over the final values of the counters. We show that the non-emptiness problem both in the deterministic and non-deterministic cases is NP-c. If the input head can move in a two-way fashion, emptiness gets undecidable, even if the pushdown stack is visibly and the automaton deterministic. We define a restriction, called the single-use restriction, to recover decid-ability in the presence of two-wayness, when the stack is visibly. This syntactic restriction enforces that any transition which increments at least one dimension is triggered only a bounded number of times per input position. Our main contribution is to show that non-emptiness of two-way visibly Parikh automata which are single-use is NExpTime-c. We finally give applications to decision problems for expressive transducer models from nested words to words, including the equivalence problem.
Document type :
Book sections
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02162279
Contributor : Luc Dartois <>
Submitted on : Friday, June 21, 2019 - 3:55:00 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:18 PM

File

Dartois2019_Chapter_Two-WayPar...
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Luc Dartois, Emmanuel Filiot, Jean-Marc Talbot. Two-Way Parikh Automata with a Visibly Pushdown Stack. Bojańczyk M., Simpson A. Foundations of Software Science and Computation Structures. FoSSaCS 2019, Springer, pp.189-206, 2019, 978-3-030-17126-1. ⟨10.1007/978-3-030-17127-8_11⟩. ⟨hal-02162279⟩

Share

Metrics

Record views

37

Files downloads

39