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Axiomatics for memory allocation

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Summary

In the paper a method of labelling is applied to constructing a correct and complete transformation system which allows one, for any program scheme, to construct systematically any permissible memory allocation for variables of the scheme. Permissible memory allocations are assumed to be such allocations that preserve all information flow connections from the initial scheme.

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Abbreviations

B :

set of internal statements (2.3)

D :

information flow graph (2.2)

D j :

component of an information flow graph (2.2)

E :

set of statements reachable downwards arcs (2.3)

G :

skeleton (2.1)

i :

input

L :

set of statements reachable upwards arcs (2.3)

N :

information carrier (2.1)

o :

output (2.1)

(o, i):

information pair (2.1)

p :

pole (2.1)

R :

memory allocation (2.1)

L :

Lavrov scheme (2.1)

T, U :

statements (2.1)

V :

poles allocation (2.1)

W :

inconsistency graph (2.3)

X :

memory (2.1)

x, y :

variables (2.1)

φ:

empty set

≻:

calculability relation (2.1)

≍:

equivalence relation (3.1)

→:

transformability relation (3.1)

█:

end of a theorem proof

ɛ:

empty word

References

  1. Yanov, Yu. I.: On logical algorithms schemata. Cybernetics Problems 1, Fizmatgiz, Moscow (1961)

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  2. Ershov, A. P.: Operator algorithms. III (On operator Yanov schemata). Cybernetics Problems 20, Nauka, Moscow (1967)

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  3. Lavrov, S. S.: On memory economy in closed program schemata. USSR Computational Mathematics and Mathematical Physics 1, no. 4 (1961)

  4. Ershov, A. P.: Reduction of the problem of the memory economy during program writing to the problem of colouring graph verticles. Doklady Akademii Nauk SSSR 142, no. 4 (1962)

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Authors and Affiliations

  1. Computing Center, 630090, Novosibirsk, USSR

    A. P. Ershov

Authors
  1. A. P. Ershov
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Additional information

The author is greatful to Miss E. L. Gorel whose research of axiomatic of generalized Yanov schemata has stimulated this writing.

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Ershov, A.P. Axiomatics for memory allocation. Acta Informatica 6, 61–75 (1976). https://doi.org/10.1007/BF00263743

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  • DOI: https://doi.org/10.1007/BF00263743

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