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Handbook of theoretical computer science (vol. A)
A Four Russians algorithm for regular expression pattern matching
Journal of the ACM (JACM)
Introduction to Automata Theory, Languages and Computability
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On the Power of Communication in Alternating Machines
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An Automata-Based Recognition Algorithm for Semi-extended Regular Expressions
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
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On the Power of Synchronization in Parallel Computations
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STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
A note on the space complexity of some decision problems for finite automata
Information Processing Letters
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Automated Software Engineering
Regular expressions: new results and open problems
Journal of Automata, Languages and Combinatorics
Succinctness of Regular Expressions with Interleaving, Intersection and Counting
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Testing extended regular language membership incrementally by rewriting
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
An effective algorithm for the membership problem for extended regular expressions
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Succinctness of regular expressions with interleaving, intersection and counting
Theoretical Computer Science
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ACM Transactions on Computational Logic (TOCL)
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Extended regular expressions (ERE) define regular languages using union, concatenation, repetition, intersection, and complementation operators. The fact ERE allow intersection and complementation makes them exponentially more succinct than regular expressions. The membership problem for extended regular expressions is to decide, given an expression r and a word w, whether w belongs to the language defined by r. Since regular expressions are useful for describing patterns in strings, the membership problem has numerous applications. In many such applications, the words w are very long and patterns are conveniently described using ERE, making efficient solutions to the membership problem of great practical interest.In this paper we introduce alternating automata with synchronized universality and negation, and use them in order to obtain a simple and efficient algorithm for solving the membership problem for ERE. Our algorithm runs in time O(m 驴 n2) and space O(m 驴 n + k 驴 n2), where m is the length of r, n is the length of w, and k is the number of intersection and complementation operators in r. This improves the best known algorithms for the problem.