Sequence Generators, Graphs, and Formal Languages

Abstract

A sequence genera tor is a finite graph, more general than , bu t akin to, the usual s t a t e d iagram associated wi th a finite au tomaton . The nodes of a sequence genera tor represen t complete s ta tes , and each node is labeled wi th an i npu t and an o u t p u t s ta te . An element of the behav ior of a sequence genera tor is ob ta ined by tak ing the inpu t and output states along an infinite path of the graph. Sequence generators may be associated with formulas of the monadic predicate calculus, in which the individual variables range over the times 0, I, 2, 3, ... , and the predicate variables represent complete states, input states, and output states. An unrestricted singulary recursion is a formula in which the complete state at time r -~ 1 is expressed as a truth-function of the complete state at time r and the input states from times T -~1 to T -~ h. Necessary and sufficient conditions are given for a formula derived from a sequence generator being equivalent to an unrestricted singulary recursion.

DOI: 10.1016/S0019-9958(62)90544-2

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Cite this paper

@article{Burks1962SequenceGG, title={Sequence Generators, Graphs, and Formal Languages}, author={Arthur W. Burks and Jesse B. Wright}, journal={Information and Control}, year={1962}, volume={5}, pages={204-212} }