Application of automata and transducers to computational semigroup theory

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In this project we will investigate applications of automata and transducers to problems in computational semigroup theory. In the short term, building on recent work of Radoszewski-Rytter we will develop a representation for words in free idempotent semigroups with good computational properties which can be used for equality testing, multiplication, and minimal word representations. In the longer term, we aim to expand this to the free objects in various varieties of semigroups. The project will consist of original theoretical research in the specified domain, reference implementations of the developed algorithms, and optimised implementation in the open source C++ library libsemigroups (https://github.com/libsemigroups/libsemigroups).