An infinite hierarchy of language families resulting from stateless pushdown automata with limited pushdown alphabets

Authors:
Alexander Meduna;Lukáš Vrábel;Petr Zemek
Affiliations:
Faculty of Information Technology, IT4Innovations, Centre of Excellence, Brno University of Technology, Brno, Czech Republic;Faculty of Information Technology, IT4Innovations, Centre of Excellence, Brno University of Technology, Brno, Czech Republic;Faculty of Information Technology, IT4Innovations, Centre of Excellence, Brno University of Technology, Brno, Czech Republic
Venue:
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Year:
2012

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Abstract

As its name suggests, a stateless pushdown automaton has no states. As a result, each of its computational steps depends only on the currently scanned symbol and the current pushdown-store top. In this paper, we consider stateless pushdown automata whose size of their pushdown alphabet is limited by a positive integer. More specifically, we establish an infinite hierarchy of language families resulting from stateless pushdown automata with limited pushdown alphabets. In addition, we prove analogous results for stateless deterministic pushdown automata and stateless real-time pushdown automata. A formulation of an open problem closes the paper.