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Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to mathematical logic .
This class is referred to as generalized cellular automata since the classical or standard cellular automata are typically defined and studied over regular graphs or grids, and the vertex functions are typically assumed to be identical. Example: Let Y be the circle graph on vertices {1,2,3,4} with edges {1,2}, {2,3}, {3,4} and {1,4}, denoted ...
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.It is an abstract machine that can be in exactly one of a finite number of states at any given time.
A Myhill graph over an alphabet A is a directed graph with vertex set A and subsets of vertices labelled "start" and "finish". The language accepted by a Myhill graph is the set of directed paths from a start vertex to a finish vertex: the graph thus acts as an automaton. [6] The class of languages accepted by Myhill graphs is the class of ...
A directed graph. A classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q 0, F): [2] [3]. Vertices Q: a finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them
In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata.These automata represent the Cayley graph of the group. That is, they can tell whether a given word representation of a group element is in a "canonical form" and can tell whether two elements given in canonical words differ by a generator.
Algorithms exist to construct and maintain such automata, [1] while keeping them minimal. DAFSA is the rediscovery of a data structure called Directed Acyclic Word Graph (DAWG), [2] although the same name had already been given to a different data structure which is related to suffix automaton. [3]
The state graph of a suffix automaton is called a directed acyclic word graph (DAWG), a term that is also sometimes used for any deterministic acyclic finite state automaton. Suffix automata were introduced in 1983 by a group of scientists from the University of Denver and the University of Colorado Boulder.