Input-Driven Pushdown Automata with Translucent Input Letters

TL;DR

This paper explores input-driven pushdown automata with translucent input letters, analyzing their computational power, closure properties, and decidability issues, revealing differences between deterministic and nondeterministic models.

Contribution

It introduces and studies the computational and closure properties of translucent input letter automata, highlighting differences from traditional models and between deterministic and nondeterministic variants.

Findings

Nondeterministic models are computationally stronger than deterministic ones.

Non-returning models surpass returning models in computational strength.

Certain decision problems are non-semidecidable in nondeterministic models.

Abstract

Input-driven pushdown automata with translucent input letters are investigated. Here, the use of translucent input letters means that the input is processed in several sweeps and that, depending on the current state of the automaton, some input symbols are visible and can be processed, whereas some other symbols are invisible, and may be processed in another sweep. Additionally, the returning mode as well as the non-returning mode are considered, where in the former mode a new sweep must start after processing a visible input symbol. Input-driven pushdown automata differ from traditional pushdown automata by the fact that the actions on the pushdown store (push, pop, nothing) are dictated by the input symbols. We obtain the result that the input-driven nondeterministic model is computationally stronger than the deterministic model both in the returning mode and in the non-returning mode, whereas it is known that the deterministic and the nondeterministic model are equivalent for input-driven pushdown automata without translucency. It also turns out that the non-returning model is computationally stronger than the returning model both in the deterministic and nondeterministic case. Furthermore, we investigate the closure properties of the language families introduced under the Boolean operations. We obtain a complete picture in the deterministic case, whereas in the nondeterministic case the language families are shown to be not closed under complementation. Finally, we look at decidability questions and obtain the non-semidecidability of the questions of universality, inclusion, equivalence, and regularity in the nondeterministic case.