While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. An initial state (time t = 0) is selected by assigning a state for each cell. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. The grid can be in any finite number of dimensions. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.Ī 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). Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. CA) is a discrete model of computation studied in automata theory. A given input string may drive a nondeterministic pushdown automaton to one of several configuration sequences if one of them leads to an accepting configuration after reading the complete input string, the latter is said to belong to the language accepted by the automaton.Gosper's Glider Gun creating " gliders" in the cellular automaton Conway's Game of Life Ī cellular automaton (pl. In general, if several actions are possible, then the automaton is called a general, or nondeterministic, PDA. If, in every situation, at most one such transition action is possible, then the automaton is called a deterministic pushdown automaton (DPDA). Put together: Given an input symbol, current state, and stack symbol, the automaton can follow a transition to another state, and optionally manipulate (push or pop) the stack. The automaton can alternatively ignore the stack, and leave it as it is. The manipulation can be to push a particular symbol to the top of the stack, or to pop off the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition. In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack.
#AUTOMATON DEFINITION FULL#
Ī nested stack automaton allows full access, and also allows stacked values to be entire sub-stacks rather than just single finite symbols.Ī finite-state machine just looks at the input signal and the current state: it has no stack to work with. Stack automata can recognize a strictly larger set of languages than pushdown automata. A stack automaton, by contrast, does allow access to and operations on deeper elements. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element.
They are more capable than finite-state machines but less capable than Turing machines (see below).ĭeterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. Pushdown automata are used in theories about what can be computed by machines. In the theory of computation, a branch of theoretical computer science, a pushdown automaton ( PDA) isĪ type of automaton that employs a stack. (Clicking on each layer gets an article on that subject)
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