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11
On the Complexity of Linear and Stratified Context Matching Problems
, 2001
"... We investigate the complexity landscape of context matching with respect to the number of occurrences of variables (i.e. linearity vs. varity 2) and various restrictions of stratification. We show that stratified context matching (SCM) and varity 2 context matching are NPcomplete, but that stratifi ..."
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Cited by 18 (1 self)
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We investigate the complexity landscape of context matching with respect to the number of occurrences of variables (i.e. linearity vs. varity 2) and various restrictions of stratification. We show that stratified context matching (SCM) and varity 2 context matching are NPcomplete, but that stratified simultaneous monadic context matching (SSMCM) is in P. SSMCM is equivalent to stratified simultaneous word matching (SSWM). We also show that the linear and the Comonrestricted case are in P and of time complexity O(n&sup3;). We give an algorithm for context matching and discuss how the performance of the general case can be improved through the use of information derived from polynomial approximations of the problem.
Program transformation by templates based on term rewriting
 In Proceedings of the 7th ACMSIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP 2005
, 2005
"... Huet and Lang (1978) presented a framework of automated program transformation based on lambda calculus in which programs are transformed according to a given program transformation template. They introduced a secondorder matching algorithm of simplytyped lambda calculus to verify whether the inpu ..."
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Cited by 8 (5 self)
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Huet and Lang (1978) presented a framework of automated program transformation based on lambda calculus in which programs are transformed according to a given program transformation template. They introduced a secondorder matching algorithm of simplytyped lambda calculus to verify whether the input program matches the template. They also showed how to validate the correctness of the program transformation using the denotational semantics. We propose in this paper a framework of program transformation by templates based on term rewriting. In our new framework, programs are given by term rewriting systems. To automate our program transformation, we introduce a term pattern matching problem and present a sound and complete algorithm that solves this problem. We also discuss how to validate the correctness of program transformation in our framework. We introduce a notion of developed templates and a simple method to construct such templates without explicit use of induction. We then show that in any program transformation by developed templates the correctness of the transformation can be verified automatically. In our framework the correctness of the program transformation is discussed based on the operational semantics. This is a sharp contrast to Huet and Lang’s framework.
Knowledge Discovery from Semistructured Texts
 Progress in Discovery Science  Final Report of the Japanese Discovery Science Project, volume 2281 of LNAI
, 2002
"... This paper surveys our recent results on the knowledge discovery from the semistructured texts. These texts contain heterogeneous structures which can be represented by labeled trees. The aim of our study is to extract useful information from the Web. First, we obtain the theoretical results on the ..."
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Cited by 8 (0 self)
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This paper surveys our recent results on the knowledge discovery from the semistructured texts. These texts contain heterogeneous structures which can be represented by labeled trees. The aim of our study is to extract useful information from the Web. First, we obtain the theoretical results on the learning rewriting rules between labeled trees. Second, we apply our method to the learning HTML trees in the framework of the wrapper induction. We also examined our algorithms for real world HTML texts and present the results.
Extracting Partial Structures from html Documents
 In Proceedings of the 14th International Florida Artificial Intelligence Research Symposium (FLAIRS2001): Knowledge Discovery and Data Mining, AAAI
, 2001
"... Abstract The new wrapper model for extracting text data from HTML documents is introduced. In this model, an HTML file is considered as an ordered labeled tree. The learning algorithm takes the sequence of pairs of an HTML tree and a set of nodes The nodes indicate the labels to extract from the HT ..."
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Cited by 7 (3 self)
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Abstract The new wrapper model for extracting text data from HTML documents is introduced. In this model, an HTML file is considered as an ordered labeled tree. The learning algorithm takes the sequence of pairs of an HTML tree and a set of nodes The nodes indicate the labels to extract from the HTML tree. The goal of the learning algorithm is to output the wrapper which exactly extracts the labels from the HTML trees.
Deterministic Secondorder Patterns
, 2004
"... Secondorder patterns, together with secondorder matching, enable concise speci cation of program transformation, and have been implemented in several program transformation systems. However, secondorder matching in general is nondeterministic, and the matching algorithm is so expensive that the ..."
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Cited by 4 (0 self)
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Secondorder patterns, together with secondorder matching, enable concise speci cation of program transformation, and have been implemented in several program transformation systems. However, secondorder matching in general is nondeterministic, and the matching algorithm is so expensive that the matching is NPcomplete. It is orthodox to impose constraints on the form of higherorder patterns so as to obtain the desirable matches satisfying certain properties such as decidability and niteness. In the context of uni cation, Miller's higherorder patterns have a single most general uni er. In this paper, we relax the restriction of his patterns without changing determinism in the context of matching instead of uni cation. As a consequence, our deterministic secondorder patterns cover a wide class of useful patterns for program transformation. The time complexity of our deterministic matching algorithm is linear in the size of a term for a xed pattern.
Automatically Computing Functional Instantiations
"... Among the standard books distributed with ACL2 is the considerhint book in the hints subdirectory, which implements a heuristic for computing functional instantiations. The implementation of the hint involves four basic algorithms: a secondorder pattern matching algorithm that can compute instanti ..."
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Among the standard books distributed with ACL2 is the considerhint book in the hints subdirectory, which implements a heuristic for computing functional instantiations. The implementation of the hint involves four basic algorithms: a secondorder pattern matching algorithm that can compute instantiations for constrained and defined functions that call constrained functions, a process for generating variants of a term obtained by applying equations, a process for extending secondorder matching through definitions so that when instantiating defined functions the algorithm can pick up appropriate bindings for the constrained functions inside the definitions, and an algorithm for sorting among likely functional substitutions. The secondorder matching algorithm is an incomplete and slightly extended implementation of the HuetLang algorithm. We describe the four basic algorithms involved in guessing functional instantiations. We briefly suggest further work required to make the utility robust and suggest a new feature that could be added to ACL2 if this utility were sufficiently robust. We hope that some enterprising user or student will take up these challenges.
Generalization Algorithms for SecondOrder Terms
"... Abstract. In this paper, we study the generalization algorithms for secondorder terms, which are treated as firstorder terms with function variables, under an instantiation order denoted by �. First,weextend the least generalization algorithm lg for a pair of firstorder terms under �, introduced ..."
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Abstract. In this paper, we study the generalization algorithms for secondorder terms, which are treated as firstorder terms with function variables, under an instantiation order denoted by �. First,weextend the least generalization algorithm lg for a pair of firstorder terms under �, introduced by Plotkin and Reynolds, to the one for a pair of secondorder terms. The extended algorithm lg, however, is insufficient to characterize the generalization for a pair of secondorder terms, because it computes neither the least nor the minimal generalization under �. Sincethetransformation rule for secondorder matching algorithm consists of an imitation and a projection, in this paper, we introduce the imitationfree generalization algorithm ifg and the projectionfree generalization algorithm pfg. Then, we show that ifg computes the minimal generalization under � of any pair of secondorder terms, whereas pfg computes the generalization equivalent to lg under �. Nevertheless, neither lg, ifg nor pfg preserves the structural information. Hence, we also introduce the algorithm spg and show that it computes a structurepreserving generalization. Finally, we show that the algorithms lg, pfg and spg are associative, while the algorithm ifg is not. 1
Deterministic Higherorder Patterns for Program Transformation
, 2003
"... Higherorder patterns, together with higherorder matching, enable concise speci cation of program transformation, and have been implemented in several program transformation systems. However, higherorder matching generally generates nondeterministic matches, and the matching algorithm is so ex ..."
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Higherorder patterns, together with higherorder matching, enable concise speci cation of program transformation, and have been implemented in several program transformation systems. However, higherorder matching generally generates nondeterministic matches, and the matching algorithm is so expensive that even secondorder matching is NPcomplete. It is orthodox to impose constraint on the form of patterns so as to obtain the desirable matches satisfying certain properties such as decidability and niteness. In the context of uni cation, Miller's higherorder patterns have a single most general uni er. We relax the restriction of his patterns without changing determinism in the context of matching instead of uni cation. As a consequence, our deterministic higherorder pattern (DHP) covers a wide class of useful patterns for program transformation. Our deterministic matching algorithm is ecient which is linear in the size of the term for a xed pattern.
Deterministic Secondorder Patterns in Program Transformation
 In International Symposium on Logicbased Program Synthesis and Transformation (LOPSTR 2003
, 2003
"... Higherorder patterns, together with higherorder matching, enable concise specification of program transformation, and have been implemented in several program transformation systems. However, higherorder matching generally generates nondeterministic matches, and the matching algorithm is so ex ..."
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Higherorder patterns, together with higherorder matching, enable concise specification of program transformation, and have been implemented in several program transformation systems. However, higherorder matching generally generates nondeterministic matches, and the matching algorithm is so expensive that even secondorder matching is NPcomplete. It is orthodox to impose constraint on the form of patterns so as to obtain the desirable matches satisfying certain properties such as decidability and finiteness. In the context of unification, Miller's higherorder patterns have a single most general unifier, while unification of general patterns is nondeterministic (and even undecidable). We relax the restriction of his patterns without changing determinism in the context of matching instead of unification. As a consequence, our deterministic secondorder pattern covers a wide class of useful patterns for program transformation. Our deterministic matching algorithm is as fast as the firstorder matching algorithm, almost in proportion to the size of the term.
Efficient SecondOrder Predicate Schema Matching Algorithm
"... A schema is an abstracted or a generalized knowledge to help with solving problems. A secondorder predicate schema matching is a problem of computing the matchers of a pair such that P is a secondorder predicate schema and p is a first order closed formula. The secondorder matching is known as NP ..."
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A schema is an abstracted or a generalized knowledge to help with solving problems. A secondorder predicate schema matching is a problem of computing the matchers of a pair such that P is a secondorder predicate schema and p is a first order closed formula. The secondorder matching is known as NPcomplete,in general. We propose a new matching algorithm based on the prechecking of the usable rules, and show that an efficient matching algorithm can be established under this approach for some classes which are important from practical view point.