# Realization of Events by Logical Nets

• Irving M. Copi
• Calvin C. Elgot
• Jesse B. Wright

## Abstract

In Representation of Events in Nerve Nets and Finite Automata [3], S. C. Kleene obtains a number of interesting results. The most important of these, his analysis and synthesis theorems (theorems 5 and 3), are obscured both by the complexity of his basic concepts and by the nature of the elements used in his nets. In this paper we give a new formulation and new proofs of Kleene’s analysis and synthesis theorems, in which we presuppose no acquaintance with Kleene’s work. We use simpler basic concepts and construct our nets out of more familiar and convenient elements (see section 4). The simplified formulation and proofs should make these important results more widely accessible. Some detailed comments on Kleene’s ideas are made in section 7.

### Keywords

Assure lIme Tate

## Preview

### References

1. [1]
A. W.Burks and H.Wang, The logic of automata, Jour. Assoc. Comp. Mach., Part I: 4 (1957), 193–218
2. [1a]
A. W.Burks and H.Wang, The logic of automata, Jour. Assoc. Comp. Mach., Part II: 4 (1957), 279–297.
3. [2]
A. W.Burks and J. B.Wright, Theory of logical nets, Proc. IRE 41 (1953), 1357–1365.
4. [3]
S. C.Kleene, Representation of events in nerve nets and finite automata, Automata Studies, edited by C. E. Shannon and J. McCarthy, Princeton University Press, 1956, pp. 3–41.Google Scholar
5. [4]
E. F.Moore, Gedanken-experiments on sequential machines, Automata Studies, edited by C. E. Shannon and J. McCarthy, Princeton University Press, 1956, pp. 129–153.Google Scholar
6. [5]
G. H.Mealy, A method for synthesizing sequential circuits, The Bell System Technical Journal, 34 (1955), 1045–1079.

© Springer-Verlag New York Inc. 1982

## Authors and Affiliations

• Irving M. Copi
• 1
• Calvin C. Elgot
• 1
• Jesse B. Wright
• 1
1. 1.University of MichiganAnn ArborUSA