This example hints slightly on the previously mentioned features of the FSA: In the world of automata, we say that the word is accepted by the automaton. If you can go from starting state to one of the end states only through transitions labeled by consecutive letters of the word, the word is in the language (set). Arrows indicate transitions and are labeled by the letters of the alphabet. State 0 is the starting state and states 4 and 7 are the end states. The circles are the states of the automaton. Here we have an automaton that stores the “wasp” and “wisp” words: Typical automaton is defined by five components: its states (like nodes in a graph), which incorporate a starting state and all end states, transitions between states (edges) and the alphabet. They are particularly interesting because the representation they use is very memory efficient and allows to recognize the word of length m in O(m) time, which is not bad considering the compact representation. In essence they can do the same job as any set data structure available in your programming language or library of choice. the algorithm for constructing minimal automata directly.įinite-state automata are data structures, which can recognize (sometimes infinite) set of words over some alphabet - we call this set a language.the algorithm for minimizing existing automata,.Introduction to constructing minimal automata containing: In the post you’ll find:Ī few words about finite-state automata with a simple implementation in Python , Have you ever wondered how Lucene/Elasticsearch does its job so well? This post will teach you about essential part of the Lucene index - minimal finite-state automaton (FSA), which allows for memory-efficient indexing of text.