S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. of 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on inductive inference. Jain and Sharma [18] analyzed the mind change complexity and the intrinsic complexity of EFSs. In contrast to the learnability of EFSs on inductive inference, the polynomial time learnability is another interesting theme on learning EFSs. For this purpose, Miyano et al. [24, 25] introduced the subclass hereditary EFS, denoted by HEFS. This class includes the class of pattern languages and is enough to express the context free languages. Furthermore, this class exactly de nes the class PTIME [17] Miyano et al. consider the learnability of the hierarchy HEFS(m; k; t; r) ....

.... queries) then it is not polynomial time learnable with equivalence queries (and membership queries) 5, 32] We denote by RP , mRP and [RP the class of regular pattern languages, at most m unions of regular pattern languages, and all nite union of regular pattern languages, respectively [12, 24, 25, 35, 36, 38]. Shinohara and Arimura [38] showed that RP and [mRP are inferable from positive data although [RP is not. On this line of studies, we show the hardness of the query learnability of these classes. The RP is not polynomial time predictable if neither are DNF formulas and the [RP is not ....

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S. Miyano, A. Shinohara, T. Shinohara, Which classes of elementary formal systems are polynomial-time learnable?, in: Proc. 1st Workshop on Algorithmic Learning Theory (Ohmsha, 1991) 139-150. 33

....hard class, hard in the consistency problem, and not polynomial time learnable. In the second table, the column for EQ PMQ is omitted since it is equivalent to EQ MQ by definition for RP and [RP. a) HEFSs with bounded variable occurrences Class MQ EQ EQ MQ EQ PMQ EQ EntMQ HEFS(m; k; t; r) poly [21] poly poly poly k bounded ESEFS no hard hard (Th15) poly [28] poly HEFS(3; k; t; r) 3] hard hard poly (Th6) poly THEFS( 3; k; 3; r) hard hard open poly (Th8) b) HEFSs with unbounded variable occurrences Class MQ EQ EQ MQ EQ EntMQ RP not PAC [22] hard ....

S. Miyano, A. Shinohara, T. Shinohara, Which classes of elementary formal systems are polynomial-time learnable?, Proc. the 1st Workshop on Algorithmic Learning Theory (1991) pp. 139--150.

....framework [44, 41, 40, 21, 31, 45, 20, 1, 16, 38, 46] They have also been studied in the PAC learning [33, 24, 39] and exact learning [11, 19, 27, 32, 33] frameworks. They are applicable to text processing [36] automated data entry systems [41] case based reasoning [22] and genome informatics [7 9, 13, 35, 42, 43]. Supported in part by NSF Grant CCR 9734940. Learning general pattern languages is a very dicult problem. In fact, even if the learner knows the target pattern, deciding whether a string can be generated by that pattern is NP complete [4, 25] Ko and Tzeng [26] showed that the consistency ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. 2nd Int. Workshop on Algorithmic Learning Theory, pages 139-150. IOS Press, 1992.

....of H is said to be acyclic if there exists a stable and terminating relation over A that is a bounding preorder for H. Page and Frisch [11] introduced a restricted subclass of local variable free clauses, called constrained clauses, which is also called hereditary clauses in Miyano et. al 1991 [16]. We denote by Atoms5 (a) the set f P (t 1 ; t r ) j P 2 5 and t 1 ; t r are subterms of a g. Definition 2 A clause (A a) is constrained if every term that occurs in the body A is also a subterm of some argument of the head a, that is, A Atoms5 (a) The arity of a program is ....

S. Miyano, A. Shinohara, T. Shinohara, Which classes of elementary formal systems are polynomial-time learnable?, In Proc. ALT'91 (1991) 139--150.

....of H is said to be acyclic if there exists a stable and terminating relation over A that is a bounding preorder for H . Page and Frisch [20] introduced a restricted subclass of local variable free clauses, called constrained clauses, which is also called hereditary clauses in Miyano et. al 1991 [18]. We denote by Atoms5 (a) the set f P (t 1 ; t r ) j P 2 5 and t 1 ; t r are subterms of a g. Definition 3. A clause (A a) is constrained if every term that occurs in the body A is also a subterm of some argument of the head a, that is, A Atoms5 (a) The arity of a program ....

....size(a) and the arity of b is bounded by constant k, we see that the cardinality and the size of ground oe (H) are both bounded by a polynomial in size(C) For any instance of a clause in ACH(k) any term appearing in the body also appears in the head. Thus, a similar argument to Miyano et al. [18] shows that H j= Coe if and only if ground oe (H) j= Coe. Since H is in ACH(k) and k is a constant, size(ground oe (H) is bounded by some polynomial in size(H) and size(C) To decide if ground oe (H) j= Coe, we can compute ground oe (H) Aoe j= aoe in polynomial time by a standard method in ....

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S. Miyano, A. Shinohara, T. Shinohara, Which classes of elementary formal systems are polynomial-time learnable?, In Proc. ALT'91 (1991) 139--150.

....time O(k d n d 1 log n) These suggest that for the inputs almost being random strings such as the biological sequences, the algorithm runs drastically faster. On the other hand, if the number of strings in word association patterns is not limited, the maximum agreement problem is NP complete [11]. Dealing with this situation, we should look for a polynomialtime algorithm that solves the problem approximately with some guaranteed approximation ratio. We partially clarify this issue by presenting the nonapproximability of maximum agreement problem of word association patterns. We show that ....

....Many Words As we have seen, Max Agreement by d Words k Proximity Association for fixed d and k is solvable in polynomial time. However, if d and k are not limited, then the problem becomes NP complete. The intractability follows the NP completeness of similar pattern search problems, for example [11]. This may be avoided in practical applications by polynomial time approximation algorithms. Consider the following trivial algorithm: Given an instance, simply count the numbers of positivelabeled strings and negative labeled strings and choose the better one from an empty pattern accepting all ....

S. Miyano, A. Shinohara and T. Shinohara, Which classes of elementary formal systems are polynomial-time learnable. Proc. 2nd Workshop on Algorithmic Learning Theory, 139-150 (1991).

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S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. of 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991.

....# # of strings. Question: Is there a string w that is a subsequence for each string s # S, but not a subsequence for any string t # T The problem can be interpreted as a special case of the finding the best subsequence pattern. The next theorem shows the problem is intractable. Theorem 2 ([13, 16, 17]) The consistency problem for subsequence patterns is NPcomplete. Therefore, we are essentially forced to enumerate and evaluate exponentially many subsequence patterns in the worst case, in order to find the best subsequence pattern. In the next section, we show a practical solution based on ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. of 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991.

....a consistent subsequence with given examples. Here, we call a subsequence s is consistent with positive strings Pos and negative strings Neg if s is a subsequence for any w # Pos and s is not a subsequence for any w # Neg. The computational complexity related to this problem was studied in [5, 8, 9]. It is shown that finding a consistent subsequence with given positive and negative examples is NP complete. In some application area, finding a subsequence that is maximally consistent with given examples is more important, because there might be no consistent subsequence in real data due to ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991.

....# # # of strings. Question: Is there a string w that is a subsequence for each string s # S, but not a subsequence for any string t # T The problem can be interpreted as a special case of the finding best subsequence pattern. The next theorem shows the problem is intractable. Theorem 2 ([13, 16, 17]) The consistency problem for subsequence patterns is NPcomplete. Therefore, we are essentially forced to enumerate and evaluate exponential by many subsequence patterns in the worst case, in order to find the best subsequence pattern. In the next section, we show a practical solution based on ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991.

....explains the examples correctly. When we use a subsequence as a rule to distinguish positive examples from negative examples, the main task is to find a subsequence which is common to positive examples but never appear in negative examples. The complexity related to this problem was studied in [5, 6, 7]. The basic problem around here is to determine whether a string s is a subsequence of a string t or not. It is almost trivial to show that the problem can be solved in O( s t ) When s is fixed, we can solve it in O( t ) time by constructing a finite automaton which accepts all strings of ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In Proc. 2nd Workshop on Algorithmic Learning Theory, pages 139--150, 1991. 10

.... time computability of a fitting for a class of polynomial Vapnik Chervonenkis dimension is sufficient for the class to be polynomial time learnable [7] Unfortunately, the consistency problem is shown to be NP complete for many hypothesis spaces such as k term DNF [8] and regular patterns [5]. To realize efficient learning algorithms, we have to overcome this computational hardness. In most studies on practical machine learning, a target hypothesis space is restricted so that the consistency problem becomes efficiently solvable. Another approach is to use information in addition to ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In S. Arikawa, A. Maruoka, and T. Sato, editors, Proc. ALT '91, pp. 139--150. JSAI, 1991.

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) Miyano, S., Shinohara, A. and Shinohara, T.: Which classes of elementary formal systems are polynomial-time learnable?, Proc. 2nd Workshop on Algorithmic Learning Theory, pp. 139--150 (1991).

....et al. 20] It is shown in [20] that even a problem for a very simple type is NP complete whether ambiguity is allowed in a motif or not since its proof works for both cases. Similar works related to the complexity issues on pattern languages are also found in Jiang and Li [10] and Miyano et al. [13]. 2. Motifs and Complexity For an alphabet 6, we denote by 6 3 the set of all strings over 6. The length of a string w in 6 3 is denoted by jwj. We denote 6 = 6 3 0 f g ( is the empty string) and 6 n = fw 2 6 3 j jwj = ng for an integer n 0. For a set S, the number of elements in ....

Miyano, S., Shinohara, A. and Shinohara, T., Which classes of elementary formal systems are polynomial-time learnable?, Proc. Second Workshop on Algorithmic Learning Theory, 1991, 139--150.

....which were introduced by Smullyan [Smu61] and proposed as a unifying framework for language learning by Arikawa et al. ASY92] can be considered as natural extensions of patterns. Even from the viewpoint of practical applications, pattern languages have been paid much attention. Miyano et al. MSS91] considered the PAC learnability of EFS languages, and showed considerably successful experiments on some identification problems in Molecular Biology [AKM 92] The weakness of inductive learning from positive data relative to that from positive and negative data is well known since the ....

S. Miyano, A. Shinohara, and T. Shinohara. Which classes of elementary formal systems are polynomial-time learnable? In S. Arikawa, A. Maruoka, and T. Sato, editors, Proceedings of the Second Workshop on Algorithmic Learning Theory, pp. 139--150, 1991.

No context found.

) Miyano, S., Shinohara, A. and Shinohara, T., \Which classes of elementary formal systems are polynomial-time learnable," In Proc. 2nd Workshop on Algorithmic Learning Theory, 139-150, 1991.

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