NP-completeness of the set unification and matching problems

Kapur, Deepak; Narendran, Paliath

doi:10.1007/3-540-16780-3_113

Cited by 73 publications

(30 citation statements)

References 4 publications

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“…This is a more general result than Theorem 7 in the paper by Kapur and Narendran [10], where they prove NP-hardness for AI-matching, where additional uninterpreted function symbols are allowed. In our proof we use only one associative and idempotent function symbol.…”

Section: Introductionmentioning

confidence: 59%

Matching Modulo Associativity and Idempotency Is NP—Complete

Klíma¹,

Srba

2000

Lecture Notes in Computer Science

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Section: Introductionmentioning

confidence: 59%

Matching Modulo Associativity and Idempotency Is NP—Complete

Klíma¹,

Srba

2000

Lecture Notes in Computer Science

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“…The efficiency of this operation is crucial to support our efficient learning of relational representations. This result should be contrasted with general hardness results for subsumption [13,27].…”

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confidence: 74%

Learning with Feature Description Logics

Cumby

Roth

2003

Inductive Logic Programming

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Abstract. We present a paradigm for efficient learning and inference with relational data using propositional means. The paradigm utilizes description logics and concepts graphs in the service of learning relational models using efficient propositional learning algorithms. We introduce a Feature Description Logic (FDL) -a relational (frame based) language that supports efficient inference, along with a generation function that uses inference with descriptions in the FDL to produce features suitable for use by learning algorithms. These are used within a learning framework that is shown to learn efficiently and accurately relational representations in terms of the FDL descriptions. The paradigm was designed to support learning in domains that are relational but where the amount of data and size of representation learned are very large; we exemplify it here, for clarity, on the classical ILP task of learning family relations. This paradigm provides a natural solution to the problem of learning and representing relational data; it extends and unifies several lines of works in KRR and Machine Learning in ways that provide hope for a coherent usage of learning and reasoning methods in large scale intelligent inference.

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“…This would result in a fairly compact index even for large vectors, at the cost of slightly more complex algorithms. This is the version implemented by Korovin in iProver 7 . However, to our knowledge no systematic evaluation has taken place so far.…”

Section: Performance In Automatic Modementioning

confidence: 99%

“…Subsumption of multi-literal clauses is an NP-complete problem [7]. If some attention is paid to the implementation, the worst case is rarely (if ever) encountered in practice, and single clause-clause subsumption tests rarely form a critical bottleneck.…”

Section: Introductionmentioning

confidence: 99%

Simple and Efficient Clause Subsumption with Feature Vector Indexing

Schulz

2013

Automated Reasoning and Mathematics

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Abstract. This paper describes feature vector indexing, a new, nonperfect indexing method for clause subsumption. It is suitable for both forward (i.e., finding a subsuming clause in a set) and backward (finding all subsumed clauses in a set) subsumption. Moreover, it is easy to implement, but still yields excellent performance in practice. As an added benefit, by restricting the selection of features used in the index, our technique immediately adapts to indexing modulo arbitrary AC theories with only minor loss of efficiency. Alternatively, the feature selection can be restricted to result in set subsumption. Feature vector indexing has been implemented in our equational theorem prover E, and has enabled us to integrate new simplification techniques making heavy use of subsumption. We experimentally compare the performance of the prover for a number of strategies using feature vector indexing and conventional sequential subsumption.

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NP-completeness of the set unification and matching problems

Cited by 73 publications

References 4 publications

Matching Modulo Associativity and Idempotency Is NP—Complete

Matching Modulo Associativity and Idempotency Is NP—Complete

Learning with Feature Description Logics

Simple and Efficient Clause Subsumption with Feature Vector Indexing

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