Digging input-driven pushdown automata

Martin Kutrib,Andreas Malcher,Markus Holzer,José M Sempere

doi:10.1051/ita/2021006

Martin Kutrib, Andreas Malcher + Show 2 more

Open Access

https://doi.org/10.1051/ita/2021006

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Abstract

Input-driven pushdown automata (IDPDA) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that popping from the empty pushdown does not block the computation but continues it with empty pushdown. Here, we consider IDPDAs that have a more balanced behavior concerning pushing and popping. Digging input-driven pushdown automata (DIDPDA) are basically IDPDAs that, when forced to pop from the empty pushdown, dig a hole of the shape of the popped symbol in the bottom of the pushdown. Popping further symbols from a pushdown having a hole at the bottom deepens the current hole furthermore. The hole can only be filled up by pushing symbols previously popped. We study the impact of the new behavior of DIDPDAs on their power and compare their capacities with the capacities of ordinary IDPDAs and tinput-driven pushdown automata which are basically IDPDAs whose input may be preprocessed by length-preserving finite state transducers. It turns out that the capabilities are incomparable. We address the determinization of DIDPDAs and their descriptional complexity, closure properties, and decidability questions.

Highlights

In connection with an upper bound for the space needed for the recognition of deterministic context-free languages, a subclass of pushdown automata has been introduced in [20]
input-driven pushdown automata (IDPDA) are defined as ordinary real-time pushdown automata whose behavior on the pushdown is solely driven by the input symbols
Among others the capacities are compared with the capacities of ordinary IDPDAs and so-called tinput-driven pushdown automata which are basically IDPDAs whose input may be preprocessed by length-preserving finite state transducers [13]

Summary

Introduction

In connection with an upper bound for the space needed for the recognition of deterministic context-free languages, a subclass of pushdown automata has been introduced in [20] These so-called input-driven pushdown automata (IDPDA) work in real time and, more importantly, in an input-driven way. IDPDAs are defined as ordinary real-time pushdown automata whose behavior on the pushdown is solely driven by the input symbols. If the pushdown has a hole, the automaton ‘sees’ the bottom of the hole, that is, the (shape of the) symbol which was popped as last These devices are called digging input-driven pushdown automata (DIDPDA) and are studied in the sequel. We would like to note that a preliminary version of this work was presented at the 11th Workshop on Non-Classical Models of Automata and Applications (NCMA 2019), Valencia, Spain, July 2–3, 2019, and it is published in [11]

Preliminaries

Computational capacity

Determinization

Closure properties and decidability questions

On the union of the families accepted by DIDPDAs and IDPDAs