Automata with Group Actions

Mikolaj Bojanczyk, Bartek Klin, Slawomir Lasota
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
Our motivating question is a Myhill-Nerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are the special case of our framework where
more » ... etters can be only compared for equality. We use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality, we obtain automata equivalent in expressive power to finite memory automata, as defined by Francez and Kaminski.
doi:10.1109/lics.2011.48 dblp:conf/lics/BojanczykKL11 fatcat:nrrsy7qxojflzf2jkm2aloesfe