Given a finite set X of points, a finite set of commuting transformations over X (generators), and another transformation f over X, we analyze the complexity of the problem of deciding whether f can be obtained by composition of the generators. We show that the complexity varies with the threshold of the semigroup: polynomial-time (NC
3 in parallel) with threshold zero or one, and NP-complete otherwise.
- Permutation Group
- Commutative Semigroup
- Parallel Complexity
- Membership Problem
- Transformation Semigroup
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