| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Research Abstract |
The purpose of this research is to construct fundamental theory of inductive learnability of Elementary Formal Systems(EFSs, for short) allowing erasing substitutions from positive examples. We have obtained the following results :
1.The language defined by the so-called Primitive Formal System(PFS, for short), which consists of a base clause and an induction clause, was shown to be expressed as a union of infinitely many regular pattern languages.
2.We obtained a necessary and sufficient condition for a PFS to be reduced. Moreover, we showed that it is efficiently decidable.
3.The inclusion problem of languages defined by reduced PFSs can he reduced to the syntactical inclusion problem of regular patterns appearing in the original PFSs.
4.We showed that there exists a finite tell-tale set of each language defined by a PFS. Moreover, we showed that the language class defined by PFSs have the property of the so-called M-finite thickness.
5.The class of languages defined by the so-called simp
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le formal systems(SFSs, for short) and regular formal systems(RFSs, for short), which are more general EFSs than PFSs, with at most k axioms is shown to be learnable in case erasing substitutions are not allowed (Shinohara 95). In this research, we showed that the above class is not learnable in case erasing substitutions are allowed.
6.Although PFSs are RFSs with just two axioms, we introduced other syntactical conditions on PFSs and showed that they are learnable from positive examples.
7.We applied the results as mentioned at 6 to the learning problem of languages generated by SH systems. An SH system is a simplified model for expressing a recombinant behavior or a splicing operation for a DNA sequence. The language generated by an SH system is a regular language with some special properties. In this research, we expressed SH languages by RFSs with empty substitutions and showed that they are learnable from positive examples by using results obtained at 6.
8.The languages defined by decision trees over regular patterns were shown to be expressed as finitely many unions and intersections of regular pattern languages and co-regular pattern languages. In this research, we showed that the language class of finitely many unions or intersections of regular pattern languages has the so-called finite elasticity and showed that the class is learnable. The problem for co-regular pattern languages is still open. Less
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