Cayley Linear-Time Computable Groups
Abstract
This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We show that the groups Z2 Z2, Z2 F2 and Thompson's group F have normal forms for which the right multiplication by a group element is computed in linear time on a 2-tape Turing machine. This refines the results previously established by Elder and the authors that these groups are Cayley polynomial-time computable.
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