Regular Expressions with Numerical Constraints and Automata with Counters

Regular expressions with numerical constraints are an extension of regular expressions, allowing to bound numerically the number of times that a subexpression should be matched. Expressions in this extension describe the same languages as the usual regular expressions, but are exponentially more succinct. We define a class of finite automata with counters and a deterministic subclass of these. Deterministic finite automata with counters can recognize words in linear time. Furthermore, we describe a subclass of the regular expressions with numerical constraints, a polynomial-time test for this subclass, and a polynomial-time construction of deterministic finite automata with counters from expressions in the subclass.

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