### Abstract

Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free $K$-grammars, to model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter $K$ this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism.
Our first result characterizes the generating capacity of these fuzzy context-free $K$-grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free $K$-grammars shares closure properties very similar to those of the family of ordinary context-free languages.
The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger- Kasami's algorithm and some recursive descent algorithms. These algorithms turn out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms.

Original language | English |
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Title of host publication | IWPT '95, Fourth International Workshop on Parsing technologies, Prague and Karlovy Vary (Czech Republic), September 20-24, 1995 |

Subtitle of host publication | workshop proceedings |

Place of Publication | Prague |

Publisher | Charles University |

Pages | 14-25 |

Number of pages | 12 |

Publication status | Published - 1995 |

Event | 4th International Workshop on Parsing Technologies, IWPT 1995 - Prague & Karlovy Vary, Czech Republic Duration: 20 Sep 1995 → 24 Sep 1995 Conference number: 4 |

### Workshop

Workshop | 4th International Workshop on Parsing Technologies, IWPT 1995 |
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Abbreviated title | IWPT |

Country | Czech Republic |

City | Prague & Karlovy Vary |

Period | 20/09/95 → 24/09/95 |

### Keywords

- HMI-SLT: Speech and Language Technology

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## Cite this

Asveld, P. R. J. (1995). A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition. In

*IWPT '95, Fourth International Workshop on Parsing technologies, Prague and Karlovy Vary (Czech Republic), September 20-24, 1995: workshop proceedings*(pp. 14-25). Prague: Charles University.