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Each model in automata theory plays important roles in several applied areas. Finite automata are used in text processing, compilers, and hardware design. Context-free grammar (CFGs) are used in programming languages and artificial intelligence. Originally, CFGs were used in the study of human languages.
Hasse diagram of some classes of quantitative automata, ordered by expressiveness. [1]: Fig.1 In theoretical computer science and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers.
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.
Automata-based programming is a programming paradigm in which the program or part of it is thought of as a model of a finite-state machine (FSM) or any other (often more complicated) formal automaton (see automata theory). Sometimes a potentially infinite set of possible states is introduced, and such a set can have a complicated structure, not ...
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running ...
Hybrid automata come in several flavors: The Alur–Henzinger hybrid automaton is a popular model; it was developed primarily for algorithmic analysis of hybrid systems model checking. The HyTech model checking tool is based on this model. The Hybrid Input/Output Automaton model has been developed more recently. This model enables compositional ...
NFAs have been generalized in multiple ways, e.g., nondeterministic finite automata with ε-moves, finite-state transducers, pushdown automata, alternating automata, ω-automata, and probabilistic automata. Besides the DFAs, other known special cases of NFAs are unambiguous finite automata (UFA) and self-verifying finite automata (SVFA).
Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q 0 is an element of Q, called the initial state. F is a set of sets of states. Formally, F ⊆ P(Q) where P(Q) is powerset of Q. F defines the acceptance condition.