Non-self-embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata

  • Bruno Guillon
  • Giovanni Pighizzini
  • Luca Prigioniero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10977)


Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and 1-limited automata to deterministic finite automata. Constant-height pushdown automata and 1-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by 1-limited automata is presented. However, the converse transformation is proved to cost exponential.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Bruno Guillon
    • 1
  • Giovanni Pighizzini
    • 1
  • Luca Prigioniero
    • 1
  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly

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