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Acta Informatica

, Volume 34, Issue 5, pp 389–410 | Cite as

A hierarchy of uniquely parsable grammar classes and deterministic acceptors

  • Kenichi Morita
  • Noritaka Nishihara
  • Yasunori Yamamoto
  • Zhiguo Zhang

Abstract.

We introduce a new class of grammars called uniquely parsable grammars (UPGs). A UPG is a kind of phrase structure grammar having a restricted type of rewriting rules, where parsing can be performed without backtracking. We show that, in spite of such restriction to the rules, UPGs are universal in their generating ability. We then define three subclasses of UPGs. They are M-UPGs (monotonic UPGs), RC-UPGs (UPGs with right-terminating and context-free-like rules), and REG-UPGs (regular UPGs). It is proved that the generating abilities of the classes of M-UPGs, RC-UPGs, and REG-UPGs are exactly characterized by the classes of deterministic linear-bounded automata, deterministic pushdown automata, and deterministic finite automata, respectively. Especially, the class of RC-UPGs gives a very simple grammatical characterization of the class of deterministic context-free languages. Thus, these four classes form a deterministic counterpart of the classical Chomsky hierarchy.

Keywords

Generate Ability Phrase Structure Finite Automaton Deterministic Finite Automaton Restricted Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Kenichi Morita
    • 1
  • Noritaka Nishihara
    • 2
  • Yasunori Yamamoto
    • 3
  • Zhiguo Zhang
    • 4
  1. 1.Faculty of Engineering, Hiroshima University, Higashi-Hiroshima-shi, 739 Japan (e-mail: morita@ke.sys.hiroshima-u.ac.jp)JP
  2. 2.Faculty of Engineering, Yamagata University, Yonezawa-shi, 992 JapanJP
  3. 3.National Museum of Ethnology, Suita-shi, 565 JapanJP
  4. 4.Lingnan College, Zhongshan University, Ghuangzhou, 510275 People's Republic of ChinaCN

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