Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
A taxonomy of problems with fast parallel algorithms
Information and Control
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The parallel complexity of Abelian permutation group problems
SIAM Journal on Computing
The word and generator problems for lattices
Information and Computation
Parallel algorithms for solvable permutation groups
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Membership testing in commutative tranformation semigroups
Information and Computation
Characterization of idempotent transformation monoids
Information Processing Letters
Automata, Languages, and Machines
Automata, Languages, and Machines
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Varieties Of Formal Languages
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Membership testing in transformation monoids
Membership testing in transformation monoids
Learning Expressions over Monoids
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Algebraic Characterizations of Small Classes of Boolean Functions
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The computing power of programs over finite monoids
Journal of Automata, Languages and Combinatorics - Selected papers of the workshop on logic and algebra for concurrency
Learning expressions and programs over monoids
Information and Computation
Learning expressions and programs over monoids
Information and Computation
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The problem of testing membership in aperiodic or “group-free” transformation monoids is the natural counterpart to the well-studied membership problem in permutation groups. The class A of all finite aperiodic monoids and the class G of all finite groups are two examples of varieties, the fundamental complexity units in terms of which finite monoids are classified. The collection of all varieties V forms an infinite lattice under the inclusion ordering, with the subfamily of varieties that are contained in A forming an infinite sublattice. For each V ⊆ A, the associated problem MEMB(V) of testing membership in transformation monoids that belong to V, is considered. Remarkably, the computational complexity of each such problem turns out to look familiar. Moreover, only five possibilities occur as V ranges over the whole aperiodic sublattice: With one family of NP-hard exceptions whose exact status is still unresolved, any such MEMB(V) is either PSPACE-complete, NP-complete, P-complete or in AC0. These results thus uncover yet another surprisingly tight link between the theory of monoids and computational complexity theory.