Matching Patterns with Variables

Manea, Florín; Schmid, Markus L.

doi:10.1007/978-3-030-28796-2_1

Cited by 7 publications

(5 citation statements)

References 77 publications

(97 reference statements)

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“…identical to checking whether D can be factorised into 𝑛 factors such that for each Z 𝑖 all factors that correspond to the variables in Z 𝑖 are the same. This is the pattern matching problem with variables (also known as the membership problem for pattern languages, or the matching problem for regular expressions with backreferences), a well-known NP-complete problem (see, e. g., [24]).…”

Section: Decision Problems For Spannersmentioning

confidence: 99%

Document Spanners - A Brief Overview of Concepts, Results, and Recent Developments

Schmid

Schweikardt

2022

Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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The information extraction framework of document spanners was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, J. ACM 2015) as a formalisation of the query language AQL, which is used in IBM's information extraction engine SystemT. Since 2013, this framework has been investigated in depth by the principles of database management community and beyond. The present paper gives a brief overview of concepts, results, and recent developments concerning document spanners. CCS CONCEPTS• Information systems → Information retrieval; • Theory of computation → Database query languages (principles); Data structures and algorithms for data management; Design and analysis of algorithms; Automata extensions; Regular languages.

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Section: Decision Problems For Spannersmentioning

confidence: 99%

Document Spanners - A Brief Overview of Concepts, Results, and Recent Developments

Schmid

Schweikardt

2022

Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…For example, the so-called membership problem (determining whether a word is a member of a pattern language) is NP-complete as shown by Ehrenfreucht and Rozenberg [30] for the erasing case, and independently by Angluin [6] for the non-erasing case. Since the membership problem in general is NP-complete, there has been work on finding classes of pattern languages for which the membership problem is tractable [17,33,79,95].…”

Section: Related Literaturementioning

confidence: 99%

“…As the membership problem for pattern languages is NP-complete, there has been some effort to find classes of patterns for which the membership problem is polynomial time [17,79,95].…”

Section: Initializationmentioning

confidence: 99%

Conjunctive Queries for Logic-Based Information Extraction

M.¹

2022

Preprint

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This thesis offers two logic-based approaches to conjunctive queries in the context of information extraction. The first and main approach is the introduction of conjunctive query fragments of the logics FC and FC [REG], denoted as FC-CQ and FC[REG]-CQ respectively. FC is a first-order logic based on word equations, where the semantics are defined by limiting the universe to the factors of some finite input word. FC [REG] is FC extended with regular constraints.Our first results consider the comparative expressive power of FC[REG]-CQ in relation to document spanners (a formal framework for the query language AQL), and various fragments of FC[REG]-CQ -some of which coincide with well-known language generators, such as patterns and regular expressions. better supervisor and mentor.I'd also like to thank the numerous people at Loughborough university who have helped me during my time here, both as an undergraduate student and a PhD student. I am grateful to Daniel Reidenbach for being my second supervisor, as well as for sparking my interest in theoretical computer science with his undergraduate module. Thank you to Andrea Soltoggio and Szymon Łopaciuk for all the interesting discussions over lunch. An additional thanks to Szymon for numerous conversations in the office about research and more. I wish to express my gratitude to Parisa Derakhshan, Iain Phillips, Robert Mercaş, Manfred Kufleitner, Dominik D. Freydenberger, and Yanning Yang for allowing me to teach their modules. Doing so has made me a more well-rounded computer scientist.I am grateful to Joel D. Day and Ana Sălăgean for agreeing to be my internal examiners, and Anthony W. Lin for being my external examiner.I would also like to thank Justin Brackemann for the helpful feedback and list of typos in the proof of Theorem 4.12.Last, but not least, I'd like to thank my family. Without all their encouragement, I would not have been able to finish this project. I can't put into words how thankful I am for my parents, my sister, and my grandparents.v Contents Abstract iiiAcknowledgements v Document Spanners. Document spanners were introduced by Fagin, Kimelfeld, Reiss, and Vansummeren [31] as a formal framework for the Annotation Query Language (or AQL) used in IBM's SystemT. Regarding data complexity, Florenzano, Riveros, Ugarte, Vansummeren, and Vrgoc [34] gave a constant-delay algorithm for enumerating the results of deterministic vset-automata, after linear time preprocessing. Amarilli, Bourhis, Mengal, and Niewerth [3] extended this result to nondeterministic vset-automata.Regarding combined complexity, Freydenberger, Kimelfeld, and Peterfreund [39] introduced regex CQs and proved that their evaluation is NP-complete (even for acyclic queries), and that fixing the number of atoms and the number of equalities in SERCQs allows for polynomial-delay enumeration of results. Freydenberger, Peterfreund, Kimelfeld, and Kröll [89] showed that non-emptiness for a join of two sequential regex formulas is NP-hard, under schemaless semantics, even for a single c...

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“…Manea and Schmid [15] described a series of results based on some efficient pattern matching techniques with variables. The authors also give the extensions of this matching with the variable problem.…”

Section: Background Workmentioning

confidence: 99%

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

2020

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AbstractPattern matching is the area of computer science which deals with security and analysis of data. This work proposes two 2D pattern matching algorithms based on two different input domains. The first algorithm is for the case when the given pattern contains only two symbols, that is, binary symbols 0 and 1. The second algorithm is in the case when the given pattern contains decimal numbers, that is, the collection of symbols between 0 and 9. The algorithms proposed in this manuscript convert the given pattern into an equivalent binary or decimal number, correspondingly find the cofactors of the same dimension and convert these cofactors into numbers if a particular cofactor number matches indicate the matching of the pattern. Furthermore, the algorithm is enhanced for decimal numbers. In the case of decimal numbers, each row of the pattern is changed to its decimal equivalent, and then, modulo with a suitable prime number changes the decimal equivalent into a number less than the prime number. If the number mismatched pattern does not exist, the complexity of the proposed algorithm is very low as compared to other traditional algorithms.

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Matching Patterns with Variables

Cited by 7 publications

References 77 publications

Document Spanners - A Brief Overview of Concepts, Results, and Recent Developments

Document Spanners - A Brief Overview of Concepts, Results, and Recent Developments

Conjunctive Queries for Logic-Based Information Extraction

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

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