Algorithmically finite groups
Copyright policy )Algorithmically finite groups
We call a group $G$ {\it 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.
- Vanderbilt University United States
- Stevens Institute of Technology United States
word problem, Generators, relations, and presentations of groups, conjugacy problem, Algebra and Number Theory, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Group Theory (math.GR), finitely generated groups, algorithms, equality problem, Dehn monsters, FOS: Mathematics, recursively presented groups, algorithmically finite groups, 20F65, Mathematics - Group Theory
word problem, Generators, relations, and presentations of groups, conjugacy problem, Algebra and Number Theory, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Group Theory (math.GR), finitely generated groups, algorithms, equality problem, Dehn monsters, FOS: Mathematics, recursively presented groups, algorithmically finite groups, 20F65, Mathematics - Group Theory
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