S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95 (1992) 97--113.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The elementary formal system (EFS, for short) was originally invented by Smullyan [39] in early 1960s to develop his recursive function theory. Professor Arikawa is a pioneer to employ such an EFS for studying formal language theory [7] in 1970. After about 20 years later, he and his partners [8, 9] characterized the EFSs as logic programs over strings and introduced a new hierarchy of various language classes, which includes the four classes of Chomsky hierarchy, the class of pattern languages, and many others. Furthermore, he enhanced EFSs as a unifying framework for language learning, by ....

.... class of HEFS( k; t; r) The learning algorithm with a top down search strategy is based on the controlled generation of candidate clauses and the contradiction backtracing algorithm of Shapiro [34] This algorithm can be regarded as a counterpart of the MIEFS of Arikawa, Shinohara, and Yamamoto [9] along a polynomial time learning model. We show that this algorithm learns all hypotheses H of HEFS( k; t; r) in polynomial time using O(p equivalence queries and O(p ) predicate membership queries for every k; t; r 0, where p is the number of predicate symbols, m is the ....

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S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, Theoret. Comput. Sci. 95(1) (1992) 97-113.

.... learning algorithms have been successfully applied toward some problems in molecular biology (see [SSS 94, SA95] Pattern languages and finite unions of pattern languages turn out to be subclasses of Smullyan s [Smu61] Elementary Formal Systems (EFSs) and Arikawa, Shinohara and Yamamoto [ASY92] show that the EFSs can also be treated as a logic programming language over strings. The investigations of the learnability of subclasses of EFSs are interesting because they yield corresponding results about the learnability of subclasses of logic programs. Hence, these results have relevance ....

S. Arikawa, T. Shinohara, and A. Yamamoto. Learning elementary formal systems. Theoretical Computer Science, 95:97--113, 1992.

....which learnability results achieved for EFSs extend to AEFSs and which do not. 1 Introduction and Motivation Elementary formal systems (EFSs) have been introduced by Smullyan [20] to develop his theory of recursive functions over strings. In [3] and in a series of subsequent publications like [5, 24, 4, 6, 19, 25, 14], for example, Arikawa and his co workers proposed elementary formal systems as a unifying framework for formal language learning. EFSs are a kind of logic programs such as a Prolog programs, for instance. EFSs directly manipulate non empty strings over some underlying alphabet and can be used to ....

.... , is the pattern which one obtains when applying to . Let C = p( 1 ; n ) be an atom and let r = A B 1 ; Bn be a rule. Then, we set C = p( 1 ; n ) and r = A B 1 ; Bn . If r is ground, then it is said to be a ground instance of r. De nition 1 ([6]) Let , and X be xed, and let be a nite set of rules over , and X. Then, S = is said to be an EFS. EFSs can be considered as particular logic programs without negation. There are two major di erences: i) patterns play the role of terms and (ii) uni cation has to be realized ....

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S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, TCS 95 (1992) 97-113.

.... based on Watson Crick complementarity can be represented by the following reaction rule: f 2 (X) X; f 1 (X) The pattern reaction system has a close relation to the elementary formal system (EFS) whose computational capability and learnability from positive data are well studied( Smu61][ASY92][Shi94] However, PRS is di erent from EFS in that it deals with a real valued multiset. Let us consider the following two chemical reactions: A 1 A 2 k 1 A 4 ; A 1 A 3 k 2 A 5 ; where k 1 and k 2 are the rate constants of the above reactions. Di erential equations to model these ....

S. Arikawa, T. Shinohara and A. Yamamoto. Learning Elementary Formal Systems. Theoretical Computer Science, 95, pp.97-113, 1992

....or not AEFSs can be learned from examples. AEFSs generalize Smullyan s [12] elementary formal systems (EFSs, for short) which he introduced to develop his theory of recursive functions. In the last years, the learnability of EFSs has intensively been studied within several formal frameworks (cf. [4, 16, 3, 5, 11, 17, 10]) 3.1 Elementary Formal Systems Next, we provide notions and notations that allow for a formalization of EFSs. Assume three mutually disjoint sets a finite set Sigma of characters, a finite set Pi of predicates, and an enumerable set X of variables. We call every element in ( Sigma [X) ....

...., oe is the pattern which one obtains when applying oe to . Let C = p( 1 ; n ) be an atom and let r = A B 1 ; Bn be a rule. Then, we set Coe = p( 1 oe; n oe) and roe = Aoe B 1 oe; Bn oe. If roe is ground, then it is said to be a ground instance of r. Definition 1 ([5]) Let Sigma , Pi, and X be fixed, and let Gamma be a finite set of rules. Then, S = Sigma; Pi; Gamma ) is said to be an EFS. EFSs can be considered as particular logic programs without negation. There are two major differences: i) patterns play the role of terms and (ii) unification has ....

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S. Arikawa, T. Shinohara, and A. Yamamoto, `Learning elementary formal systems ', Theoretical Computer Science, 95, 97--113, (1992).

....of elementary formal systems using equivalence queries and membership queries. An elementary formal system (EFS) was originally invented by Smullyan [37] in early 1960s to develop his recursive function theory. Arikawa [6] first employed EFS for studying formal languages, and later, Arikawa et al. [8] showed that EFS can be regarded as logic programs over strings, and that several subclasses of EFS correspond to Chomsky hierarchy and other important language classes in inductive inference, e.g. pattern languages [8, 14, 34] Then, they developed in a uniform way inductive inference algorithms ....

.... first employed EFS for studying formal languages, and later, Arikawa et al. 8] showed that EFS can be regarded as logic programs over strings, and that several subclasses of EFS correspond to Chomsky hierarchy and other important language classes in inductive inference, e.g. pattern languages [8, 14, 34]. Then, they developed in a uniform way inductive inference algorithms for these language classes based on the theory of model inference systems (MIS) by Shapiro [29] This shows that EFS provide a unifying framework for studying the learnability of a wide range of diverse language classes ....

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S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95(1) (1992) pp. 97--113.

.... algorithms have been successfully applied for solving problems in molecular biology (cf. e.g. Shimozono et al. 36] Shinohara and Arikawa [39] Pattern languages and finite unions of pattern languages turn out to be subclasses of Smullyan s [41] elementary formal systems (EFS) Arikawa et al. [3] have shown that EFS can also be treated as a logic programming language over strings. Recently, the techniques for learning finite unions of pattern languages have been extended to show the learnability of various subclasses of EFS (cf. Shinohara [38] From a theoretical point of view, ....

S. Arikawa, T. Shinohara, and A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95 (1992), 97--113. REFERENCES 30

.... pattern language learning algorithms have been successfully applied for solving problems in molecular biology (see [SSS 94, SA95] Pattern languages and finite unions of pattern languages [Shi83, Wri89] turn out to be subclasses of Smullyan s [Smu61] Elementary Formal Systems (EFSs) ASY92] show that the EFSs can also be treated as a logic programming language over strings. The techniques for learning finite unions of pattern languages have been extended to show the learnability of various subclasses of EFSs [Shi91] Investigations of the learnability of subclasses of EFSs are ....

S. Arikawa, T. Shinohara, and A. Yamamoto. Learning elementary formal systems. Theoretical Computer Science, 95:97--113, 1992.

....to the graph isomorphism problem for 0 GI . 1 Introduction A formal graph system (FGS) 21] is a kind of logic programs which deals with graphs just like terms [10] By regarding terms as trees, conventional logic programs can be directly simulated by FGSs. Moreover, an elementary formal system [2, 3, 18], that is a logic program on strings, is also a special case of FGSs. We have shown in [21] that a family of graphs is generated by a hyperedge replacement grammar (HRG) 7, 8] if and only if it is defined by a regular FGS that is an FGS of a very simple form. This result implies that some ....

S. Arikawa, T. Shinohara, and A. Yamamoto. Learning elementary formal systems. Theoretical Computer Science, 95:97--113, 1992.

....conceptions of CFL s A few researchers have attacked the problem by using representations of CFL s that are not based on grammars. Yokomori gives an algorithm that learns context free expressions [Yok88a] and Arikawa et al. present a method for inferring regular elementary formal systems [ASY92]. Both these papers bring solutions from other domains to bear on the problem of CFL inference; however, their techniques have not yielded polynomial time algorithms. Let L be a CFL. Define a substitution (f a (L) as the set of strings gen7 erated by taking every string w 2 L and replacing all ....

S. Arikawa, T. Shinohara, and A. Yamamoto, "Learning elementary formal systems," Theoret. Comput. Sci 2(1), 91--113 (1992) ,

....in the limit from positive data. Elementary formal systems (EFS s, for short) originally introduced by Smullyan [Smu61] are a kind of logic system where we use string patterns instead of terms in first order logic. For more detailed definition or theoretical results on learning EFS s, refer to [ASY92], Shi94] By LB, we denote the class of all length bounded EFS s. By LB n , we denote the class of length bounded EFS s with at most n axioms. We denote, by L(LB) L(LB n ) the class of all languages defined by EFS s in LB (LB n ) with a fixed unary predicate symbol. It is known that ....

S. Arikawa, T. Shinohara and A. Yamamoto. Learning Elementary Formal Systems. Theoretical Computer Science, 95, pp.97-113, 1992

.... algorithms have been successfully applied for solving problems in molecular biology (cf. e.g. Shimozono et al. 36] Shinohara and Arikawa [39] Pattern languages and finite unions of pattern languages turn out to be subclasses of Smullyan s [41] elementary formal systems (EFS) Arikawa et al. [3] have shown that EFS can also be treated as a logic programming language over strings. Recently, the techniques for learning finite unions of pattern languages have been extended to show the learnability of various subclasses of EFS (cf. Shinohara [38] From a theoretical point of view, ....

S. Arikawa, T. Shinohara, and A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95 (1992), 97--113. 30 J. Case, S. Jain, S. Lange and T. Zeugmann

.... Introduction Machine learning methods have been developed in [1, 2] to discover bioinformatical knowledge from amino acid sequences of proteins which are compiled together with their functional information in databases such as PIR [13] The learning algorithm in [1] uses elementary formal systems [3] as the representation of concepts and the learning algorithm in [2] produces decision trees over regular patterns as hypotheses. Both learning algorithms assume two sets of strings called the set of positive examples and the set of negative examples, and find a hypothesis which explains the ....

Arikawa, S., Shinohara, T. and Yamamoto, A., "Learning elementary formal systems," Theor. Comput. Sci., vol. 95, pp. 97--113, 1992

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) Arikawa, S., Shinohara, T., and Yamamoto, A., "Learning Elementary Formal Systems," Theoretical Computer Science, 95, pp. 97-113, 1992.

....as is the resolution principle in logic programming. In recent years, as a new framework for inductive inference of formal languages, elementary formal systems(EFSs for short) proposed by Smullyan[12] have been proved to be useful and powerful in language learning from positive data by Arikawa[3, 4, 5] and Shinohara[11] in the criterion of Gold s identification in the limit. There are two main differences between logic programs and EFSs. The first is the structure of term; in logic programs, terms are defined as the combinations of function symbols with variables and constants with some other ....

....algorithm based on IR. Finally, conclusions are given in section 6. 2 PRELIMINARIES (1) Elementary Formal Systems Suppose 6, X and 5 be mutually disjoint sets. Let 6 be a finite set, X a set of variables, and 5 a set of predicate symbols (suppose all with arity one, for general see Arikawa[4, 5]) We call 6 alphabet, denote its elements by a, b, c, 1 1 1, and X as variable, denote its elements by x, y, z, x 1 , y 1 , 1 1 1 and each element of 5 as predicate symbol, denote by p, q, p 1 , p 2 , 1 1 1, where each of them has an arity. Let 6 3 be the set of all words over 6, and 6 be ....

S. Arikawa, T. Shinohara and A. Yamamoto: "Learning Elementary Formal Systems", Theoretical Computer Science, Vol.95, No.1, 1992, pp. 97-- 113.

.... is so simple, it has been considered as a very important class for studies on inductive learning [LW91, Muk92] For example, elementary formal systems (EFSs for short) 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 ....

....complete refinement operator for OE, S be a finite set of objects, and p be a covering of S. Then cspc(S; p) and tr(p; S) are computable in polynomial time in jpj and jSj. 6 Applications to pattern languages First we present an efficient and complete refinement operator ae for regular patterns [ASY92] We define the size of a pattern p by size(p) 22jpj 0 ]v(p) where v(p) is the set of variables appearing in p. Clearly size(p) 2 2 jpj and jpj size(p) for any p. A substitution is said to be basic for a regular pattern p, if satisfies one of the following: ffl = fx : ag, where x 2 ....

S. Arikawa, T. Shinohara, and A. Yamamoto. Learning elementary formal systems. Theoretical Computer Science, Vol. 95, pp. 97--113, 1992.

....learning method to protein motif discovery [2, 3, 9] but most of these methods require negative examples in addition to positive examples. For example, Arikawa et al. 2] reported a knowledge acquisition system for finding motifs from amino acid sequences based on Elementary Formal Systems [4]. Their system produced a set of regular patterns of high accuracy from randomly chosen positive and negative examples. This paper proposes an efficient method for learning protein motif from positive examples. A set S of positive examples e 1 WLVNFIIVIMVFILFLVGLYLL e 2 ....

S. Arikawa, T. Shinohara, and A. Yamamoto. Learning elementary formal systems. Theoretical Computer Science, 95, pp. 97--113, 1992.

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S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95 (1992) 97--113.

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