The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M. For string compression, straight-line programs, i.e., context-free grammars that generate a single string, are used in this paper. It is shown that the compressed word problem for a free inverse monoid of finite rank at least two is complete for Π2p (second universal level of the polynomial time hierarchy). Moreover, it is shown that there exists a fixed finite idempotent presentation (i.e., a finite set of relations involving idempotents of a free inverse monoid), for which the corresponding quotient monoid has a PSPACE-complete compressed word problem. The ordinary uncompressed word problem for such a quotient can be solved in logspace [10]. Finally, a PSPACE-algorithm that checks whether a given element of a free inverse monoid belongs to a given rational subset is presented. This problem is also shown to be PSPACE-complete (even for a fixed finitely generated submonoid instead of a variable rational subset). © 2011 Springer-Verlag GmbH.
CITATION STYLE
Lohrey, M. (2011). Compressed word problems for inverse monoids. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 448–459). https://doi.org/10.1007/978-3-642-22993-0_41
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