Abstract
We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid \(\mathcal M\), and we ask whether these two words represent the same monoid element of \(\mathcal M\). For compression we use straight-line programs. For several classes of monoids we obtain completeness results for complexity classes in the range from P to EXPSPACE. As a by-product of our results on compressed word problems we obtain a fixed deterministic context-free language with a PSPACE-complete membership problem. The existence of such a language was open so far. Finally, we investigate the complexity of the compressed membership problem for various circuit complexity classes.
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