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Unary Pushdown Automata and Auxiliary Space Lower Bounds

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

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Abstract

It is well-known that context-free languages defined over a one letter alphabet are regular. This implies that unary pushdown automata and unary context-free grammars can be transformed into equivalent nondeterministic and deterministic finite automata. In this paper, we state some upper bounds on the number of states of the resulting automata, with respect to the size of the descriptions of the given pushdown automata and context-free grammars. As a main consequence, we are able to prove a log log n lower bound for the workspace used by one-way auxiliary pushdown automata in order to accept nonregular unary languages. The notion of space we consider is the so called weak space.

Partially supported by MURST, under the project “Modelli di calcolo innovativi: metodi sintattici e combinatori”.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Universitá degli Studi di Milano, via Comelico 39, 20135, Milano, Italy

    Giovanni Pighizzini

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  1. Giovanni Pighizzini
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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Pighizzini, G. (2000). Unary Pushdown Automata and Auxiliary Space Lower Bounds. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_55

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  • DOI: https://doi.org/10.1007/3-540-44612-5_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

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