## On the Learnability of Recursively Enumerable Languages from Good Examples (1997)

Venue: | Theoret. Comput. Sci |

Citations: | 1 - 1 self |

### BibTeX

@ARTICLE{Jain97onthe,

author = {Sanjay Jain and Steffen Lange and Jochen Nessel},

title = {On the Learnability of Recursively Enumerable Languages from Good Examples},

journal = {Theoret. Comput. Sci},

year = {1997},

volume = {261}

}

### OpenURL

### Abstract

The present paper investigates identification of indexed families of recursively enumerable languages from good examples. In the context of class preserving learning from good text examples, it is shown that the notions of finite and limit identification coincide. On the other hand, these two criteria are different in the context of class comprising learning from good text examples. In the context of learning from good informant examples, finite and limit identification criteria differ for both class preserving and class comprising cases. The above results resolve an open question posed by Lange, Nessel and Wiehagen in a similar study about indexed families of recursive languages. 1 Introduction Consider the identification of formal languages from positive data. A machine is fed all the strings and no nonstrings of a language L, in any order, one string at a time. The machine, as it receives strings of L, outputs a sequence of grammars. The machine is said to identify L just ...

### Citations

3824 | Introduction to Automata Theory Languages and Computation,Second Edition - HOPCROFT, MOTAWANI, et al. |

889 |
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- Gold
- 1967
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837 |
Theory of recursive functions and effective computability
- Rogers
- 1967
(Show Context)
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- Angluin
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259 |
Toward a mathematical theory of inductive inference
- Blum, Blum
- 1975
(Show Context)
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Finding patterns common to a set of strings
- Angluin
- 1980
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92 |
Machine inductive inference and language identification
- Case, Lynes
- 1982
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59 |
Prudence and other conditions on formal language learning
- Fulk
- 1990
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- Goldman, Mathias
- 1996
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Citation Context ...mples and not necessarily just the good examples. This avoids some trivial cases where learnability can be achieved by a suitable encoding of a correct grammar into the good examples (see for example =-=[BCJ95]-=-). The model places as an additional requirement that it has to be possible to effectively generate the good examples for a language (using its grammar). This allows a helpful teacher to provide the g... |

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- 1993
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Citation Context ...rom good informant examples. It is open at present whether InfBc is contained in class comprising learning in the limit from good informant examples. We now proceed formally. 3 We refer the reader to =-=[deJK96]-=- for some nice characterizations for learnability of indexed families of recursively enumerable languages, along the lines of characterizations for learnability of indexed families of recursive langua... |

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Citation Context ...attern p, we can take fw 2 \Sigma j jwj = jpj; w 2 L(p)g as a set of good examples for L(p) (for class preserving finite identification from good text examples) 2 . We refer the reader to [FKW93] and =-=[LNW94]-=- for additional motivation and discussion on these models. Learning from good examples was first considered by Freivalds, Kinber and Wiehagen in the context of function learning [FKW93]. Lange, Nessel... |