Factorization forests of finite height
Theoretical Computer Science - Special issue on theoretical computer science, algebra and combinatorics
XPath evaluation in linear time
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The Height of Factorization Forests
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
ACM Computing Surveys (CSUR)
XPath evaluation in linear time with polynomial combined complexity
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Algorithms for regular languages that use algebra
ACM SIGMOD Record
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In the first part of the paper, we propose an algorithm which inputs an NFA A and a word a1 ... an, does a precomputation, and then answers queries of the form: "is the infix ai ... aj accepted by A?". The precomputation is in time poly(A) ċ n, and the queries are answered in time poly(A). This improves on previous algorithms that worked with the exponentially less succinct DFA's or monoids. In the second part of the paper, we propose a transducer model for data trees. We show that the transducer can be evaluated in linear time. We use this result to evaluate XPath queries in linear time. The algorithms in both parts of the paper use factorization forests.