The parallel complexity of Abelian permutation group problems
The authors classify Abelian permutation group problems with respect to their parallel complexity. For such groups specified by generating permutations the authors show that testing membership, computing order and testing isomorphism are NC/sup 1/-equivalent to (and therefore have essentially the same parallel complexity as) determining solvability of a system of linear equations modulo a product of small prime powers; they show that intersecting two such groups is NC/sup 1/-equivalent to computing setwise stabilizers; they show that each of these problems is NC/sup 1/-reducible to the problem of computing a generator-relator presentation. Then the authors prove that the aforementioned problems belong to NC/sup 3/, thus identifying several natural set recognition problems in NC which may lie outside NC/sup 2/. Finally they prove that NC/sup 4/ contains the problem of computing the cyclic decomposition of an Abelian permutation group. Background results include an NC/sup 1/ solution to the problem of computing the product of n integers modulo a (log n)-bit integer, and an NC/sup 1/ reduction from the problem of computing a path between two nodes in a graph to that of determining accessibility of one node from another.
- Research Organization:
- Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal, Montreal, Quebec H3C 3J7
- OSTI ID:
- 5793262
- Journal Information:
- SIAM J. Comput.; (United States), Journal Name: SIAM J. Comput.; (United States) Vol. 16:5; ISSN SMJCA
- Country of Publication:
- United States
- Language:
- English
Similar Records
Predecessor and permutation existence problems for sequential dynamical systems
Predecessor and permutation existence problems for sequential dynamical systems