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Easy constructions in complexity theory: Gap and speed-up theorems. (English) Zbl 0328.68044


MSC:

68Q25 Analysis of algorithms and problem complexity
03D20 Recursive functions and relations, subrecursive hierarchies
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References:

[1] Leonard Bass and Paul Young, Ordinal hierarchies and naming complexity classes, J. Assoc. Comput. Mach. 20 (1973), 668 – 686. · Zbl 0339.68038 · doi:10.1145/321784.321793
[2] Manuel Blum, A machine-independent theory of the complexity of recursive functions., J. Assoc. Comput. Mach. 14 (1967), 322 – 336. · Zbl 0155.01503 · doi:10.1145/321386.321395
[3] Manuel Blum, On effective procedures for speeding up algorithms, J. Assoc. Comput. Mach. 18 (1971), 290 – 305. · Zbl 0221.02016 · doi:10.1145/321637.321648
[4] A. Borodin, Computational complexity and the existence of complexity gaps, J. Assoc. Comput. Mach. 19 (1972), 158 – 174; corrigendum, ibid. 19 (1972), 576. · Zbl 0261.68024 · doi:10.1145/321679.321691
[5] Robert L. Constable, The operator gap, J. Assoc. Comput. Mach. 19 (1972), 175 – 183. · Zbl 0229.68016 · doi:10.1145/321679.321692
[6] J. Hartmanis and J. E. Hopcroft, An overview of the theory of computational complexity, J. Assoc. Comput. Mach. 18 (1971), 444 – 475. · Zbl 0226.68024 · doi:10.1145/321650.321661
[7] John P. Helm, On effectively computable operators, Z. Math. Logik Grundlagen Math. 17 (1971), 231 – 244. · Zbl 0245.02036
[8] John Helm and Paul Young, On size vs. efficiency for programs admitting speed-ups, J. Symbolic Logic 36 (1971), 21 – 27. · Zbl 0258.68023 · doi:10.2307/2271512
[9] E. McCreight and A. Meyer, Classes of computable functions defined by bounds on computation, Proc. First Annual ACM Sympos. on Theory of Computing, pp. 79-88. · Zbl 1283.03074
[10] Albert R. Meyer and Patrick C. Fischer, Computational speed-up by effective operators, J. Symbolic Logic 37 (1972), 55 – 68. · Zbl 0249.68018 · doi:10.2307/2272545
[11] A. Meyer and R. Moll, Honest bounds for complexity classes of recursive functions, Project MAC Report, April 1972. · Zbl 0322.02038
[12] Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967.
[13] Paul Young, Speed-ups by changing the order in which sets are enumerated, Math. Systems Theory 5 (1971), 148 – 156. · Zbl 0218.68004 · doi:10.1007/BF01702871
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