Tinput-Driven Pushdown Automata

Abstract

AbstractIn input-driven pushdown automata (\(\text {IDPDA}\)) the input alphabet is divided into three distinct classes and the actions on the pushdown store (push, pop, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDPDA}\) is preprocessed by a deterministic sequential transducer. These automata are called tinput-driven pushdown automata (\(\text {TDPDA}\)) and it turns out that \(\text {TDPDA}\)s are more powerful than \(\text {IDPDA}\)s but still not as powerful as real-time deterministic pushdown automata. Nevertheless, even this stronger model has still good closure and decidability properties. In detail, it is shown that \(\text {TDPDA}\)s are closed under the Boolean operations union, intersection, and complementation. Furthermore, decidability procedures for the inclusion problem as well as for the questions of whether a given automaton is a \(\text {TDPDA}\) or an \(\text {IDPDA}\) are developed. Finally, representation theorems for the context-free languages using \(\text {IDPDA}\)s and \(\text {TDPDA}\)s are established.KeywordsInput driven pushdown automataSequential transducersReal-time deterministic context-free languagesClosure propertiesDecidability questions