Automatic Processing of Natural and Formal Languages

In the most outstanding theoretical advance, theories of language and of automata have been joined through one series of theorems establishing within each realm hierarchies of increasing power and by another series of theorems correlating machines with the languages they may either generate or recognize. Machines are ordered in terms of computing power by placing one above the other if everything that can be computed by the lower machine can also be computed by the upper machine but there exists a computation which the upper can do that the lower cannot. The two best known types of machines—finite state automata and Turing machines—respectively mark the lower and upper boundary of the range of computing power. A finite state machine, as its name implies, is one whose configuration or state at any one time is selected from among a finite number of possible states. In the absence of other restrictions, any machine with an infinite number of states or, alternatively, a storage capacity which, though finite at any time, can keep growing beyond any bound as required in the course of operation essentially has the computing power of a Turing machine. Although real computing machines are obviously always finite, describing them in the formalism of the theory of finite state machines does not provide as clear an insight into their properties as one might wish. This is one reason for the growth, within the theory of automata, of descriptions of machines in which a basically finite state control element is supplemented by an actually or potentially infinite storage device, usually an abstraction of the notion of n tapes capable of growing beyond any bound and subject to a variety of restrictions on reading or writing ability and on direction of motion. Most interesting among these in the present context is the so-called pushdown store automaton which, typically, is a finite state device augmented by a tape on which both reading and writing is permitted, motion is allowed in both directions but scanning is limited to only the one symbol immediately on top of the tape, visualized as extending downward potentially without limit. A symbol further down on the tape may be reached but only at the price of erasing all symbols above it. This access discipline is often described as "last in first out." Machines are further distinguished as deterministic or nondeterministic. Roughly speaking, a machine is deterministic if the function of current state and current input which determines the next state and the next reading or writing action is singlevalued and nondeterministic if this function is multivalued. In addition to or instead of restrictions on the amount of storage or number of states allowable, machines may also be restricted as to the time (usually measured as number of steps) allowable in a computation. One category of time-restricted machine of current interest is the real-time machine which, given input at a constant rate, must produce a result within a fixed delay after entry of the last input item. In the last three years research on both