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Sur le nombre de registres nécessaires à l’évaluation d’une expression arithmétique. (French) Zbl 0547.68041

Summary: The distribution of the variable ”number of registers required for evaluating an arithmetic expression” on binary trees is studied in a purely combinatorial way. A new recurrence relation is proved. This relation gets a new proof, without calculations, of the theorem of Flajolet, Raoult and Vuillemin linking this distribution to the distribution of the ”left height” of a binary tree.

MSC:

68W30 Symbolic computation and algebraic computation
05C05 Trees
11A55 Continued fractions
11B37 Recurrences
68R10 Graph theory (including graph drawing) in computer science
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References:

[1] 1. A. P. ERSHOV, On progamming of arithmetic operations, CACM, vol. 1, n^\circ 8, 1958, p. 3-6. Zbl0086.33203 · Zbl 0086.33203
[2] 2. P. FLAJOLET, Combinatorial aspects of continued fractions, Discrete Math., vol. 32, 1980, p. 125-161. Zbl0445.05014 MR592851 · Zbl 0445.05014
[3] 3. P. FLAJOLET, Analyses d’algorithmes de manipulation d’arbres et de fichiers, Cahiers du B.U.R.O., p. 34-35, 1981.
[4] 4. P. FLAJOLET et J. FRANÇON, Notes non publiées.
[5] 5. P. FLAJOLET, J. C. RAOULT et J. VUILLEMIN, The number of registers required for evaluating arithmetic expressions, Theor. Comp. Sc, vol. 9, 1979, p. 99-125. Zbl0407.68057 MR535127 · Zbl 0407.68057
[6] 6. J. FRANÇON, Des codes pour arbres binaires, Actes du 2e Colloque de Lille, Les arbres en algèbre et en programmation, 17-19 février 1977. Zbl0367.94038 · Zbl 0367.94038
[7] 7. J. FRANÇON et G. VIENNOT, Permutations selon leurs pics, creux, doubles montées et doubles descentes, nombres d’Euler et nombres de Genocchi, Discrete Math., vol. 28, 1979, p. 21-35. Zbl0409.05003 MR542933 · Zbl 0409.05003
[8] 8. R. E. HORTON, Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology, Bull. of the Geological Soc. of America, vol. 56 1945, p. 275-370.
[9] 9. R. KEMP, The average number of registers needed to evaluate a binary tree optimally, Acta Informatica, vol. 11 1979, p. 363-372. Zbl0395.68059 MR533482 · Zbl 0395.68059
[10] 10. D. E. KNUTH, The Art of Computer Programming, vol. 1, Addison-Wesley, 1968. Zbl0191.17903 MR378456 · Zbl 0191.17903
[11] 11. O. PERRON, Die Lehre von den Kettenbrüchen, Teubner, Leipzig und Berlin, 1929. JFM55.0262.09 · JFM 55.0262.09
[12] 12. R. SETHI et J. D. ULLMAN, The generation of optimal codefor arithmetic expressions, JACM, vol. 17, 1970, p. 715-728. Zbl0212.18802 MR275722 · Zbl 0212.18802
[13] 13. P. S. STEVENS, Patterns in Nature, Little, Brown and Co., 1974. Traduction française : Les formes dans la nature, Seuil, Paris, 1978.
[14] 14. A. N. STRAHLER, Hypsometric (area-altitude) analysis of erosional topology, Bull. of the Geological Soc. of America, vol. 63 1952, p. 1117-1142.
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