Word Problems Solvable in Logspace
Journal of the ACM (JACM)
Complexity of Language Recognition Problems for Compressed Words
Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa
On the Parallel Complexity of Tree Automata
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Testing Equivalence of Morphisms on Context-Free Languages
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Word Problems and Membership Problems on Compressed Words
SIAM Journal on Computing
Inverse monoids: Decidability and complexity of algebraic questions
Information and Computation
Tilings and Submonoids of Metabelian Groups
Theory of Computing Systems
Leaf languages and string compression
Information and Computation
Compressedword problems for inverse monoids
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Efficient computation in groups via compression
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Processing compressed texts: a tractability border
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Compressedword problems for inverse monoids
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Hi-index | 0.00 |
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., contextfree 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).