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The equivalence problem for Kleene's regular expressions has several effective solutions, all of which are computationally inefficient. In 1, we showed that this inefficiency is an inherent property of the problem by showing that the problem of membership in any arbitrary context-sensitive language was easily reducible to the equivalence problem for regular expressions. We also showed that with a squaring abbreviation ( writing (E)2 for E×E) the equivalence problem for expressions required computing space exponential in the size of the expressions.
Stockmeyer et al. (Mon,) studied this question.