Abstract
Starting from the idea that simple functions will show some regular behaviour, we introduce the notion of sequential representation to formalize a nonuniform way of decribing such regularities, e.g. periodically repeating sequences of values. In order to obtain classes of sequentially represented functions, general conditions are given that guarantee closure under substitution and (restricted forms of) primitive recursion. Use of several restrictions for verification as well as suitable reduction methods yield specifications of classes of primitive recursive functions which contain P or PSPACE. Any precise complexity results, however, seem to require additional investigations, and remain open questions.
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References
Bel'tyukov, A.P.: A machine description and the hierarchy of initial Grzegorczyk classes, Transl. Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Stekl. AN SSSR 88 (1979), pp. 30–46
Cobham, A.: The intrinsic computational complexity of functions, ICLMPS '64, North-Holland, Amsterdam (1964), pp. 24–30
Grzegorczyk, A.: Some classes of recursive functions, Rozprawy MatematiczneIV, Warszawa 1953
Kleine Büning, H.: Note on the ɛ 1* − ɛ 2* problem, ZMLG 28 (1982), pp. 277–284
Péter, R.: Rekursive Funktionen, Akadémiai Kiadó, Budapest 1951, 2nd rev. ed. 1957
Ritchie, R.W.: Classes of predictably computable functions, TAMS 106 (1963), pp. 139–173
Thompson, D.B.: Subrecursiveness: machine independent notions of computability in restricted time and storage, MST 6 (1972), pp. 3–15
Wagner, K.: Bounded recursion and complexity classes, MFCS '79, LNCS 74 (1979), pp. 492–498
Wagner, K. & Wechsung, G.: Computational Complexity, D. Reidel, Dordrecht (1986), §10
Wette, E.: Sequentielle Darstellungen primitiv rekursiver Funktionen und Komplexitätsklassen, Dissertation, Duisburg (1989)
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Wette, E. (1990). Sequential representation of primitive recursive functions, and complexity classes. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '89. CSL 1989. Lecture Notes in Computer Science, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52753-2_56
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DOI: https://doi.org/10.1007/3-540-52753-2_56
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