## Flow Diagrams, Turing Machines and Languages with only Two Formation Rules (1966)

Venue: | Communications of the ACM |

Citations: | 141 - 0 self |

### BibTeX

@ARTICLE{Jacopini66flowdiagrams,,

author = {Giuseppe Jacopini},

title = {Flow Diagrams, Turing Machines and Languages with only Two Formation Rules},

journal = {Communications of the ACM},

year = {1966},

volume = {9},

pages = {366--371}

}

### Years of Citing Articles

### OpenURL

### Abstract

In the first part of the paper, flow diagrams are introduced to represent inter ah mappings of a set into itself. Although not every diagram is decomposable into a finite numbm of given base diagrams, this becomes hue at a semantical level due to a suitable extension of the given set and of the basic mappings defined in it. Two normalization methods of flow diagrams are given. The first has |hree base diagrams; the second, only two. In the second part of the paper, the second method is ap-plied to 'lhe theory of Turing machines. With every Turing maching provided with a two-way half-tape, ihere is associ-ated a similar machine, doing essentially 'lhe same job, but working on a tape obtained from the first one by interspersing alternate blank squares. The new machine belongs to the family, elsewhere introduced, generated by composition and iteration from the two machines X and R. That family is a proper subfamily of the whole family of Turing machines.

### Citations

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Citation Context ...low them to be decomposed into base diagrams of three types (first result) or of two types (second result). In the second part of the paper (by C. BShm), some results of a previous paper are reported =-=[8]-=- and the results of the first part of this paper are then used to prove that every Turing machine is reducible into, or in a deternfined sense is equivalent to, a program written in a language which a... |

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Nuove tecniche di progrummazione semplificanti la sintesi di macchine universuli di
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Citation Context ...ntified. 370 Communications of the ACM Volume 9 / Number 5 / May, 1966sis now extended to a mapping y ~ y* as follows: if y* ~ ... []UK_i[_2]UK... Obviously, and therefore (t, y)* ~-"''[DUK--~DUK "", =-=(9)-=- (f, Y)* ~ "''DU~--lClUK''" • M C ~ M ~ ~(~,[h,R,a,T,F,K}) M* C ~'* ~ ~l* C ~(o0", {x*, R*, c~*, T*, F*, K*} ). It is only necessary to prove that ~(~*, {X*, R*, a*, T*, F*, K*}) c ~(a, {h, R}). First... |