Tabulation Techniques for Recursive Programs

ACM Computing Surveys (CSUR)

Volumn 12, Issue 4, 1980, Pages 403-417

  Bird, R S ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

dynamic programming; pebble games; program transformation; recursion elimination; recursive functions; redundancy; tabulation

Indexed keywords

EID: 84976779750     PISSN: 03600300     EISSN: 15577341     Source Type: Journal    
DOI: 10.1145/356827.356831     Document Type: Article

References (26)

1. Aho, A. V., and Ullman, J. D., The theory of parsing, translation and compiling, vol. 1, Parsing, Prentice-Hall, Englewood Cliffs, N.J., 1972.
2. Aho, A. V., Hopcroft, J. E., and Ullman, J. D. The design and analysis of computer algorithms, Addison-Wesley, Reading, Mass., 1975.
3. Bellman, R. E. Dynamic programming, Princeton University Press, Princeton, N.J., 1957.
4. Bird, R. S. “Notes on recursion elimination,” Commun. ACM 20, 6 (June 1977), 434-439.
5. Bird, R. S. “Improving programs by the introduction of recursion,” Commun. ACM 20, 11 (Nov. 1977), 856-863.
6. Burstall, R. M., and Darlington, J. “Some transformations for developing recursive programs,” in Proc. 1975 Internat. Conf. Reliable Software, Los Angeles, 1975, pp. 465-472.
7. Chandra, A. K. “Efficient compilation of linear recursive programs,” in Conference Record, IEEE 14th Ann. Symp. Switching and Automata Theory, 1973, pp. 16-25.
8. Cohen, N. H. “Characterization and elimination of redundancy in recursive programs,” in 6th Ann. Symp. Principles of Programming Languages, 1979, pp. 143-157.
9. Hirschberg, D. S. “A linear space algorithm for computing maximal common subsequences,” Commun. ACM 18, 6 (June 1975), 341-343.
10. Horowitz, E., and Sahni, S. Fundamentals of computer algorithms, Fearon-Pitman, Belmont, Calif., 1979.
11. Knuth, D. E. The art of computer programming, vol. 2, Addison-Wesley, Reading, Mass., 1969.
12. McCarthy, J. “On efficient ways of evaluating certain recursive functions,” Project MAC A.I. Memo 32 (undated), M.I.T., Cambridge, Mass.
13. McCarthy, J. “A basis for a mathematical theory of computation,” in Computer programming and formal systems, E. Braffort and D. Hirschberg (Eds.), North-Holland, Amsterdam, 1963, pp. 33-70.
14. Michie, D. “Memo functions: A Ianguage feature with rote learning properties,” DMIP Memo. MIP-R-29, Edinburgh. 1967.
15. Partsch, H., and Pepper, P. “A family of rules for recursion removal related to the Towers of Hanoi problem,” Inf. Process. Lett. 5, 6 (Dec. 1976), 174-177.
16. Paterson, M. S., and Hewitt, C. E. “Comparative schematology,” in Record of Project MAC Conf. on Concurrent Systems and Parallel Computation, 1970, pp. 119-127.
17. Paul, W. J., and Tarjan, R.-E. “Time-space trade-offs in a pebble game,” Acta Inf. 10 (1978), 111-115.
18. Pippenger, N. “A time-space tradeoff,” J. ACM 25, 4 (1978), 509-515.
19. Reingold, E. M., Nievergelt, J., and Deo, N. Combinatorial algorithms: Theory and practice, Prentice-Hall, Englewood Cliffs, N.J., 1977.
20. Shortt, J. “An iterative program to calculate Fibonacci numbers in O(log n) arithmetic operations,” Inf. Process. Lett. 7, 6 (Oct. 1978), 299-303.
21. Steinbruggen, R. “Equivalent recursive definitions of certain number theoretical functions,” TUM-INFO-7714, Technische Univ. München, West Germany, 1977.
22. Voroboyov, N. N. The Fibonacci numbers, D. C. Heath, Boston, Mass., 1966.
23. Walker, S. A. “Some graph games related to the efficient calculation of expressions,” IBM Res. Rep. RC-3628, 1971.
24. Watanabe, O. “Another application of recursion introduction,” Inf. Process. Lett. 10, 3 (1980), 116-119.
25. Wells, M. B. Elements of combinatorial computing, Pergamon Press, Elmsford, N.Y., 1971.
26. Wirth, N. Algorithms+data structures = programs, Prentice-Hall, EngleWood Cliffs, N.J., 1976.