Abstract
We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the poly-time, linear exponential-time and doubly linear exponential time computable functions. As a consequence, we also characterize the linear space computable functions.
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References
Bellantoni, S., Cook, S.: A new recursion-theoretic characterization of the polytime functions. Computational Complexity 2, 97–110 (1992)
Ben Cherifa, A., Lescanne, P.: Termination of rewriting systems by polynomial interpretations and its implementation. Science of computer Programming 9, 131–159 (1987)
Cichon, E.A., Lescanne, P.: Polynomial interpretations and the complexity of algorithms. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 139–147. Springer, Heidelberg (1992)
Cobham, A.: The intrinsic computational difficulty of functions. In: Bar-Hillel, Y. (ed.) Proceedings of the International Conference on Logic, Methodology, and Philosophy of Science, pp. 24–30. North-Holland, Amsterdam (1962)
Dershowitz, N., Jouannaud, J.P.: Rewrite systems. Handbook of Theoretical Computer Science, vol. B. North-Holland, Amsterdam
Giesl, J.: Generating polynomial orderings for termination proofs. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 427–431. Springer, Heidelberg (1995)
Gurevich, Y.: Algebras of feasible functions. In: Twenty Fourth Symposium on Foundations of Computer Science, pp. 210–214. IEEE Computer Society Press, Los Alamitos (1983)
Hofbauer, D., Lautemann, C.: Termination proofs and the length of derivations. In: RTA-1988. LNCS, vol. 355
Lankford, D.S.: On proving term rewriting systems are Noetherien. Technical Report Memo MTP-3, louisiana Technical University, Ruston, LA (1979)
Leivant, D.: Predicative recurrence and computational complexity I: Word recurrence and poly-time. In: Clote, P., Remmel, J. (eds.) Feasible Mathematrics II, Birkhauser-Boston (1994)
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Bonfante, G., Cichon, A., Marion, J.Y., Touzet, H. (1999). Complexity Classes and Rewrite Systems with Polynomial Interpretation. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_25
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DOI: https://doi.org/10.1007/10703163_25
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