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On Learning Unions of Pattern Languages and Tree Patterns [chapter]

Sally A. Goldman, Stephen S. Kwek
1999 Lecture Notes in Computer Science  
ÒÓÒ Ó Ø Ø ÖÑ Ò Ð ×ÝÑ ÓÐ× Ò Ø × Ñ Ü Ñ Ð ×Ù ×ØÖ Ò Ó Ø ÖÑ Ò Ð ×ÝÑ ÓÐ× × Ò Ò × Ø Ò Ø ÑÙ×Ø ÔÔ Ö Ò × « ¼ · ¼ « ¼ ·½ ½℄º ÁÒ ÓØ Ö ÛÓÖ ×¸ØÓ ÒÓÒ Ó Ø Ø ÖÑ Ò Ð ×ÝÑ ÓÐ× Ò Ø Ø Ö Ø × Ò Ö ÔÐ ¸ Ø × ×ÙAE ÒØ Ò Ò ×× ÖÝ ØÓ  ...  Ò Ð ×ÝÑ ÓÐ ÒÒÓØ Ò º Ì Û Ø× Ò « Ö ÒØ ÓÖ « Ö ÒØ Ø ÖÑ Ò Ð ×ÝÑ ÓÐ׺ Ë Ñ Ð ÖÐÝÛ Ò Ð×Ó ×× Ò Ô Ò ÐØÝ ØÓ Ú ÓÐ Ø ÓÒ Ó Ø ÖÙÐ Ø Ø Ô Ö Ó Ú Ö Ð ×ÝÑ ÓÐ×¸Ó Ø × Ñ Ú Ö Ð ¸ÑÙ×Ø ×Ù ×Ø ØÙØ Ý Ø × Ñ Ø ÖÑ Ò Ð ×ØÖ Ò º Á Ø Ô  ... 
doi:10.1007/3-540-46769-6_29 fatcat:fhmpxeblhnf4nm6aooxzg74zxq

On learning unions of pattern languages and tree patterns in the mistake bound model

Sally A. Goldman, Stephen S. Kwek
2002 Theoretical Computer Science  
We present e cient on-line algorithms for learning unions of a constant number of tree patterns, unions of a constant number of one-variable pattern languages, and unions of a constant number of pattern  ...  Also, our approach is quite general and we give results to learn a class that generalizes pattern languages.  ...  In particular, we presented e cient on-line algorithms for learning unions of a constant number of tree patterns, unions of a constant number of one-variable pattern languages, and unions of a constant  ... 
doi:10.1016/s0304-3975(01)00402-9 fatcat:awgzad7vgbfaniqmq6hmw72b5q

Page 8166 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Every intersection of finitely many pattern languages can be represented as a union of pattern languages, but it may be a union of infinitely many ones.  ...  We consider the class PL‘ of unions of at most k intersections of finitely many pattern languages.  ... 

Decision lists over regular patterns

Steffen Lange, Jochen Nessel
2003 Theoretical Computer Science  
The paper introduces the notion of decision lists over regular patterns. This formalism provides a strict extension of regular erasing pattern languages and of containment decision lists.  ...  Moreover, we study the learnability of the resulting language class within di erent formal settings including Gold's model of learning in the limit as well as Valiant's model of approximately correct learning  ...  This formalism provides a strict extension of the regular erasing pattern languages, on the one hand, and of containment decision lists, on the other hand (cf. [19, 15] ).  ... 
doi:10.1016/s0304-3975(02)00419-x fatcat:nncb46j3q5fwtpj54iyy2qniwq

Learning unions of tree patterns using queries

Hiroki Arimura, Hiroki Ishizaka, Takeshi Shinohara
1997 Theoretical Computer Science  
We also show some lower bound results on the number of queries, and apply our result to learning restricted version of logic programs whose computational mechanisms are only disjunctive definition and  ...  This paper investigates efficient learning of TPk, the class of collections of at most k firstorder terms, where each collection defines the union of the sets of ground instances of each first-order term  ...  ., and Osamu Watanabe for comments and suggestions on this issue. They are very grateful to Thomas Zeugmann, who made some suggestions to improve Theorem 9 in Section 4.  ... 
doi:10.1016/s0304-3975(97)00015-7 fatcat:3gd4ew5mrngkplzbsfmp7q4gza

Learning unions of tree patterns using queries [chapter]

Hiroki Arimura, Hiroki Ishizaka, Takeshi Shinohara
1995 Lecture Notes in Computer Science  
We also show some lower bound results on the number of queries, and apply our result to learning restricted version of logic programs whose computational mechanisms are only disjunctive definition and  ...  This paper investigates efficient learning of TPk, the class of collections of at most k firstorder terms, where each collection defines the union of the sets of ground instances of each first-order term  ...  ., and Osamu Watanabe for comments and suggestions on this issue. They are very grateful to Thomas Zeugmann, who made some suggestions to improve Theorem 9 in Section 4.  ... 
doi:10.1007/3-540-60454-5_29 fatcat:tgnuyluhj5do7ok4dyhy2d73le

Learning of Finite Unions of Tree Patterns with Internal Structured Variables from Queries [chapter]

Satoshi Matsumoto, Takayoshi Shoudai, Tetsuhiro Miyahara, Tomoyuki Uchida
2002 Lecture Notes in Computer Science  
We consider the polynomial time learnability of finite unions of ordered tree patterns with internal structured variables, in the query learning model of Angluin (1988) .  ...  We show that any finite union of languages defined by m term trees is exactly identifiable in polynomial time using at most 2mn 2 restricted subset queries and at most m + 1 equivalence queries, where  ...  Learning Finite Unions of Term Tree Languages In this section, we show that finite unions of term tree languages are learnable exactly by queries.  ... 
doi:10.1007/3-540-36187-1_46 fatcat:lucm5s6o6faz5eopuuj7u6qcxi

Characteristic Sets for Inferring the Unions of the Tree Pattern Languages by the Most Fitting Hypotheses [chapter]

Yen Kaow Ng, Takeshi Shinohara
2006 Lecture Notes in Computer Science  
In this paper we show how to determine such a size for the unions of the tree pattern languages, and hence allowing us to learn the class using hypotheses that fulfill the two mentioned notions of minimality  ...  A tree pattern p is a first-order term in formal logic, and the language of p is the set of all the tree patterns obtainable by replacing each variable in p with a tree pattern containing no variables.  ...  Yen Kaow Ng is supported by the Japanese Government Scholarship of the Ministry of Education, Science, Sports, Culture and Technology of Japan.  ... 
doi:10.1007/11872436_25 fatcat:mdou7gvcjjexbgylk2rix35sqm

Learning of Finite Unions of Tree Patterns with Internal Structured Variables from Queries

S. MATSUMOTO, T. SHOUDAI, T. UCHIDA, T. MIYAHARA, Y. SUZUKI
2008 IEICE transactions on information and systems  
key words: exact learning, computational learning theory, finite union of tree pattern languages 1.  ...  The new ordering on vertices in the linear term tree f'=f{x:= [g1, [u1, u'1]], y:=[g2, [u2, u'2]]}• PAPER Special Section on Foundations of Computer Science Learning of Finite Unions of Tree Patterns  ... 
doi:10.1093/ietisy/e91-d.2.222 fatcat:6r2bja6ndvh6vfup3ifdhbqxbq

Elementary formal systems, intrinsic complexity, and procrastination

Sanjay Jain, Arun Sharma
1996 Proceedings of the ninth annual conference on Computational learning theory - COLT '96  
It is shown that the class of languages formed by taking unions of up to n+1 pattern languages is a strictly more difficult learning problem than the class of languages formed by the union of up to n pattern  ...  Examples of these classes are Angluin's pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by lengthbounded elementary formal systems studied by  ...  Shinohara [Shi86] showed that pattern languages are not closed under union, and hence it is useful to study identification of languages that are unions of more than one pattern language, as they can  ... 
doi:10.1145/238061.238093 dblp:conf/colt/JainS96 fatcat:hhf2x657qvaz3cvn7j6bmmiolu

Elementary Formal Systems, Intrinsic Complexity, and Procrastination

Sanjay Jain, Arun Sharma
1997 Information and Computation  
It is shown that the class of languages formed by taking unions of up to n+1 pattern languages is a strictly more difficult learning problem than the class of languages formed by the union of up to n pattern  ...  Examples of these classes are Angluin's pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by lengthbounded elementary formal systems studied by  ...  Shinohara [Shi86] showed that pattern languages are not closed under union, and hence it is useful to study identification of languages that are unions of more than one pattern language, as they can  ... 
doi:10.1006/inco.1996.2614 fatcat:4ntnaenvfzgoxfkpiwzi2j734i

Page 3353 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
, the class of unions becomes super-finite, that is, it con- tains all the finite languages and at least one infinite language.  ...  In this paper, we consider several restrictions on patterns in order to investigate the inferability of unbounded unions of their languages from positive data.  ... 

Finding minimal generalizations for unions of pattern languages and its application to inductive inference from positive data [chapter]

Hiroki Arimura, Takeshi Shinohara, Setsuko Otsuki
1994 Lecture Notes in Computer Science  
A pattern is a string of constant symbols and variables. The language dened by a pattern p is the set of constant strings obtained from p by substituting nonempty constant strings for variables in p.  ...  As results several classes of unions of pattern languages are shown to be polynomial time inferable from positive data.  ...  In this paper rst-order terms are called tree patterns and sets of their ground instances tree pattern languages.  ... 
doi:10.1007/3-540-57785-8_178 fatcat:nqbeqsqs5fap7ndi6ref4jnocu

Page 9545 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “We present efficient on-line algorithms for learning unions of a constant number of tree patterns, unions of a constant number of one-variable pattern languages, and unions of a con- stant number  ...  Louis, MO); Kwek, Stephen S. (1-TXSA-C; San Antonio, TX) On learning unions of pattern languages and tree patterns in the mistake bound model.  ... 

Page 7117 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
In particular, the authors show that the class of unions of < n + 1 pattern languages is harder to learn than the class of unions of < n pattern languages.  ...  In particular, the authors show that the class 68R_ Discrete mathematics in relation to computer science 97k:68130 of unions of <n pattern languages can be learned with w”" mind changes but no fewer.  ... 
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