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A pushdown table machine can be simulated by a computer in time n log log n where n is the number of table machine operations. A finite state table machine can be simulated in linear time.
The stochastic sequential machine is invariably treated as the stochastic extension of the completely-specified deterministic machine. This paper investigates the incompletely-specified finite-state stochastic sequential machine from the viewpoint of machine equivalence and reduction. Definitions are chosen and procedures developed so that they reduce to the conventional froms in the special cases...
A new model of abstract automata is presented employing the concept of finite automata on a network. Each normal network n provided with a one-way input tape determines a family of languages nl. A representation theorem, analogous to the Chomsky-Schützenberger representation theorem for context free languages1, is proved for the class nl. One consequence is that nl is a principal full AFL generated...
An n-dimensional bug-automation is generalization of a finite state acceptor to n-dimensions. With each bug B, we associate the language L(B) which is the set of top rows of the n-dimensional rectangular arrays accepted by B. One-dimensional bugs define trivially the regular sets. Twodimensional bugs define precisely the context-sensitive languages, while bugs of dimension 3 or greater define all...
The problem of assigning a probability to each string of a language L(G) generated by a grammar G is considered. Two methods are considered. One method assigns a probability to each production associated with G and the other assigns the probabilities on the basis of particular features of the language. Several necessary conditions that must be satisfied by these probability assignment techniques if...
A context-sensitive grammar G is said to be CS(k) iff a particular kind of table-driven parser, Jk(G), exists. Corresponding to each Jk(G), we define a class of parsers Jk(G). Jk(G) is itself a Jk(G). The main results are: 1. Any processor Jk(G) for a CS(k) grammar G accepts exactly the sentences of G. 2. The set of languages generable by CS(k) grammars is exactly the set of languages accepted by...
This paper develops techniques for establishing a lower bound on the number of arithmetic operations necessary for sets of simple expressions. The techniques are applied to matrix multiplication. A modification of Strassen's algorithm is developed for multiplying n × p matrices by p × q matrices. The techniques are used to prove that this algorithm minimizes the number of multiplications for a few...
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