Abstract
We call a group G algorithmically finite if no algorithm can produce an infinite set of pairwise distinct elements of G. We construct examples of recursively presented infinite algorithmically finite groups and study their properties. For instance, we show that the Equality Problem is decidable in our groups only on strongly (exponentially) negligible sets of inputs.
Original language | English |
---|---|
Pages (from-to) | 2789-2796 |
Number of pages | 8 |
Journal | Journal of Pure and Applied Algebra |
Volume | 215 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2011 |