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Sublinear time algorithms represent a new paradigm in computing, where analgorithm must give some sort of an answer after inspecting only a smallportion of the input. The most typical situation where sublinear timealgorithms are considered is property testing. There are several interestingcontexts where one can test properties in sublinear time. A canonical exampleis graph colorability. To tell that a given graph is not k-colorable, it isoften sufficient to inspect just one vertex with incident edges: if the degreeof a vertex is greater than k, then the graph is not k-colorable. It is achallenging and interesting task to find algebraic properties that could betested in sublinear time. In this paper, we address several algorithmicproblems in the theory of groups and semigroups that may admit sublinear timesolution, at least for "most" inputs.

Sublinear time algorithms in the theory of groups and semigroups