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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.
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Submitted on : Friday, June 21, 2019 - 3:55:00 PM
Last modification on : Wednesday, March 16, 2022 - 3:12:54 AM


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Luc Dartois, Emmanuel Filiot, Jean-Marc Talbot. Two-Way Parikh Automata with a Visibly Pushdown Stack. FOSSACS 2019, Apr 2019, Pragues, Czech Republic. pp.189-206, ⟨10.1007/978-3-030-17127-8_11⟩. ⟨hal-02162279⟩



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