Regular expressions into finite automata
Theoretical Computer Science
One-unambiguous regular languages
Information and Computation
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Rewriting Regular Inequalities (Extended Abstract)
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
Regular expression types for XML
ACM Transactions on Programming Languages and Systems (TOPLAS)
Ambiguity in Graphs and Expressions
IEEE Transactions on Computers
Inclusion Test Algorithms for One-Unambiguous Regular Expressions
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Efficient asymmetric inclusion between regular expression types
Proceedings of the 12th International Conference on Database Theory
Efficient inclusion for a class of XML types with interleaving and counting
DBPL'07 Proceedings of the 11th international conference on Database programming languages
The inclusion problem for regular expressions
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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This paper presents a polynomial-time algorithm for the inclusion problem for a large class of regular expressions. The algorithm is not based on construction of finite automata, and can therefore be faster than the lower bound implied by the Myhill-Nerode theorem. The algorithm automatically discards irrelevant parts of the right-hand expression. The irrelevant parts of the right-hand expression might even be 1-ambiguous. For example, if r is a regular expression such that any DFA recognizing r is very large, the algorithm can still, in time independent of r, decide that the language of ab is included in that of (a+r)b. The algorithm is based on a syntax-directed inference system. It takes arbitrary regular expressions as input. If the 1-ambiguity of the right-hand expression becomes a problem, the algorithm will report this. Otherwise, it will decide the inclusion problem for the input.