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Topological dynamics and recognition of languages (1306.1468v1)
Published 6 Jun 2013 in cs.FL, math.CO, and math.GR
Abstract: We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this context. For rational languages this reduces to the usual theory of finite automata and finite monoids.