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Neumann wrote a paper entitled "The general and logical theory of automata" for the Hixon Symposium in 1948. [11] Ulam was the one who suggested using a discrete system for creating a reductionist model of self-replication. [8]: 3 [12]: xxix Ulam and von Neumann created a method for calculating liquid motion in the late 1950s. The driving ...
Automata theory is closely related to formal language theory. In this context, automata are used as finite representations of formal languages that may be infinite. Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata.
Further, clocks can be reset. Timed automata are a sub-class of a type hybrid automata. Timed automata can be used to model and analyse the timing behavior of computer systems, e.g., real-time systems or networks. Methods for checking both safety and liveness properties have been developed and intensively studied over the last 20 years.
Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions.
Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q 0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q 0 is the initial state of the automaton, and F is the set of accepting ...
In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially ...
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).
Research in learning automata can be traced back to the work of Michael Lvovitch Tsetlin in the early 1960s in the Soviet Union. Together with some colleagues, he published a collection of papers on how to use matrices to describe automata functions. Additionally, Tsetlin worked on reasonable and collective automata behaviour, and on automata ...