## Regular Inference as a graph coloring problem (1997)

Venue: | In Workshop on Grammar Inference, Automata Induction, and Language Acquisition (ICML' 97 |

Citations: | 7 - 1 self |

### BibTeX

@INPROCEEDINGS{Coste97regularinference,

author = {François Coste and Jacques Nicolas},

title = {Regular Inference as a graph coloring problem},

booktitle = {In Workshop on Grammar Inference, Automata Induction, and Language Acquisition (ICML' 97},

year = {1997},

pages = {9--7}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the problem of learning the set of all most general DFA consistent with a labeled sample. The paper proposess a constraints based specification of the set of solutions and gives an efficient algorithm to build the system of constraints. The effective production of DFA may then be reduced to a graph coloring problem. We have implemented and tested our approach on a classical benchmark. First results are very encouraging and show that the production of all solution DFAs may be practically tractable. Keywords Regular inference, deterministic finite state automata, version space, graph coloring. Introduction The paper addresses the issue of inferring all the solutions of a regular inference problem. More precisely, the problem may be stated as follows: Given a set of positive sentences I + a set of negative sentences I \Gamma Find the set of all automata A verifying: 1. A is a deterministic finite state automata ; 2. I + is structurally complete for A ; 3. L(A), the langua...

### Citations

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Citation Context ..., or with an optimization method (Dupont 1994). The problem has been proven NP-complete in the worst case (Angluin 1978; Kearns & Valiant 1989). Our approach is related to the version space approach (=-=Mitchell 1982-=-) where all solutions of a learning problem are characterized using two sets: the set S of maximally specific solutions and the set G of maximally general solutions. In our case, S may be built straig... |

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Citation Context ... PTA. Experimentation We have used a benchmark described in (Dupont 1996) for a first validation of ideas developed in this paper. We have implemented algorithm 2 using a version of DSATUR algorithm (=-=Br'elaz 1979-=-) for the coloring step. Results are summarized in the following table. #s/#t characterizes the size of target automata in terms of number of states and transitions, #G is the mean number of automata ... |

310 | Cryptographic limitations on learning boolean formulae and finite automata
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Citation Context ...tegy (Oncina & Garcia 1992), a beam search strategy (Miclet & de Gentille 1994), or with an optimization method (Dupont 1994). The problem has been proven NP-complete in the worst case (Angluin 1978; =-=Kearns & Valiant 1989-=-). Our approach is related to the version space approach (Mitchell 1982) where all solutions of a learning problem are characterized using two sets: the set S of maximally specific solutions and the s... |

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Citation Context ... F + and a state of F \Gamma , the same inconsistency appears. For instance, in the previous example, merging state 3; 4 and 8 leads to a non deterministic automata. If this automata is determinized (=-=Aho & Ullman 1972-=-), a set of new states, ff3; 4; 8g; f3; 4; 5; 8g; f3; 4; 8; 12g; f3; 4; 6; 8; 12gg, corresponding to subsets of the previous set of states, are created. Since inconsistent pair (6; 8) occurs in the ne... |

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Citation Context ...n these conditions, the search space is finite and may be partially ordered. Most of proposed algorithms focus on the production of a single solution. They proceed either with a depth first strategy (=-=Oncina & Garcia 1992-=-), a beam search strategy (Miclet & de Gentille 1994), or with an optimization method (Dupont 1994). The problem has been proven NP-complete in the worst case (Angluin 1978; Kearns & Valiant 1989). Ou... |

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Citation Context ...pth first strategy (Oncina & Garcia 1992), a beam search strategy (Miclet & de Gentille 1994), or with an optimization method (Dupont 1994). The problem has been proven NP-complete in the worst case (=-=Angluin 1978-=-; Kearns & Valiant 1989). Our approach is related to the version space approach (Mitchell 1982) where all solutions of a learning problem are characterized using two sets: the set S of maximally speci... |

41 | Polynomial-time learning with version spaces, in
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Citation Context ...& Ball 1987; Giordano 1993). When the language of generalization consists of vectors of attribute-value pairs, several authors have proposed to manage an implicit representation of the version space (=-=Hirsh 1992-=-; Nicolas 1993; Sebag 1994). In the same spirit, we propose a compact representation of G, based on the set of admissible merging of states (Coste & Nicolas 1997). We show that such a set may be repre... |

38 | Grammatical Inference from Positive and Negative Samples by Genetic Search: the GIG Method
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Citation Context ...cus on the production of a single solution. They proceed either with a depth first strategy (Oncina & Garcia 1992), a beam search strategy (Miclet & de Gentille 1994), or with an optimization method (=-=Dupont 1994-=-). The problem has been proven NP-complete in the worst case (Angluin 1978; Kearns & Valiant 1989). Our approach is related to the version space approach (Mitchell 1982) where all solutions of a learn... |

16 | An incremental interactive algorithm for regular grammar inference
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Citation Context ...ry few authors have studied the characterization of G. Miclet has proposed in (Miclet & de Gentille 1994) a heuristic algorithm. An incremental approach using membership queries has been proposed in (=-=Parekh & Honavar 1996-=-). Preliminary studies have also been tried in the context free case (Vanlehn & Ball 1987; Giordano 1993). When the language of generalization consists of vectors of attribute-value pairs, several aut... |

9 |
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Citation Context ...int characterization of the G set. We propose in the fourth section an algorithm for an effective production of automata elements of G. The results of a first experimentation on a classical benchmark(=-=Dupont 1996-=-) are given in the fifth section. It is the first time to our knowledge, that a characterization of the whole set of solutions is proposed for this benchmark. We conclude with a sketch of various trac... |

7 | Inférence Grammaticale à partir d’Exemples et de Contre-Exemples : deux Algorithmes Optimaux (BIG et RIG) et une Version Heuristique (BRIG), Actes des JFA-94 - Miclet, Gentile - 1994 |

5 |
Une repr'esentation efficace pour les espaces de versions
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Citation Context ... Giordano 1993). When the language of generalization consists of vectors of attribute-value pairs, several authors have proposed to manage an implicit representation of the version space (Hirsh 1992; =-=Nicolas 1993-=-; Sebag 1994). In the same spirit, we propose a compact representation of G, based on the set of admissible merging of states (Coste & Nicolas 1997). We show that such a set may be represented with a ... |

4 |
Espace des versions et inf'erence de grammaires alg'ebriques
- Giordano
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(Show Context)
Citation Context ...istic algorithm. An incremental approach using membership queries has been proposed in (Parekh & Honavar 1996). Preliminary studies have also been tried in the context free case (Vanlehn & Ball 1987; =-=Giordano 1993-=-). When the language of generalization consists of vectors of attribute-value pairs, several authors have proposed to manage an implicit representation of the version space (Hirsh 1992; Nicolas 1993; ... |

4 |
Une approche par contraintes de l'espace des versions
- Sebag
- 1994
(Show Context)
Citation Context ...). When the language of generalization consists of vectors of attribute-value pairs, several authors have proposed to manage an implicit representation of the version space (Hirsh 1992; Nicolas 1993; =-=Sebag 1994-=-). In the same spirit, we propose a compact representation of G, based on the set of admissible merging of states (Coste & Nicolas 1997). We show that such a set may be represented with a set of unequ... |

2 | What is the search space of the regular inference ? ICGI'94, Grammatical inference and Applications 25--37 - Dupont, Miclet, et al. - 1994 |

1 | Inf'erence grammaticale r'eguli`ere : caract'erisation des solutions canoniques dans l'espace des fusions
- Coste, Nicolas
- 1997
(Show Context)
Citation Context ...an implicit representation of the version space (Hirsh 1992; Nicolas 1993; Sebag 1994). In the same spirit, we propose a compact representation of G, based on the set of admissible merging of states (=-=Coste & Nicolas 1997-=-). We show that such a set may be represented with a set of unequality constraints and we give an efficient algorithm to build the elements of G, reducing the problem to the coloring of the graph of c... |