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Generalised dynamic ordinals — universal measures for implicit computational complexity

Published online by Cambridge University Press:  31 March 2017

Zoé Chatzidakis
Affiliation:
Université de Paris VII (Denis Diderot)
Peter Koepke
Affiliation:
Rheinische Friedrich-Wilhelms-Universität Bonn
Wolfram Pohlers
Affiliation:
Westfälische Wilhelms-Universität Münster, Germany
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Logic Colloquium '02 , pp. 48 - 74
Publisher: Cambridge University Press
Print publication year: 2006

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References

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[3] Arnold, Beckmann, A note on universal measures for weak implicit computational complexity Logic for Programming, Artificial Intelligence, and Reasoning (Matthias Baaz and Andrei Voronkov, editors), Lecture Notes in Computer Science, vol. 2514, Springer, Berlin, 2002, pp. 53–67.
[4] Arnold, Beckmann, Dynamic ordinal analysis Archive for Mathematical Logic, vol. 42 (2003), no. 4, pp. 303–334.
[5] Arnold, Beckmann, Height restricted constant depth LK, Research Note Report TR03-034, Electronic Colloquium on Computational Complexity, 2003, http://www.eccc.uni-trier.de/eccc-reports/2003/TR03-034/.
[6] Samuel R., Buss, Bounded Arithmetic, Studies in Proof Theory. Lecture Notes, vol. 3, Bibliopolis, Naples, 1986.
[7] Samuel R., Buss, Axiomatizations and conservation results for fragments of bounded arithmetic Logic and Computation (Pittsburgh, PA, 1987) (Wilfried, Sieg, editor), ContemporaryMathematics, vol. 106, AMS, Providence, RI, 1990, pp. 57–84.Google Scholar
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[9] Samuel R., Buss and Jan, Krajíček, An application of Boolean complexity to separation problems in bounded arithmetic Proceedings of the London Mathematical Society. Third Series, vol. 69 (1994), no. 1, pp. 1–21.
[10] Johan, Håstad, Almost optimal lower bounds for small depth circuits Randomness and Computation, vol. 5 (1969), pp. 143–170.
[11] Johan, Håstad, Computational Limitations of Small Depth Circuits,MIT Press, Cambridge, MA, 1987.
[12] Jan, Johannsen, A note on sharply bounded arithmetic Archive for Mathematical Logic, vol. 33 (1994), no. 2, pp. 159–165.
[13] Jan, Krajíček, Fragments of bounded arithmetic and bounded query classes Transactions of the American Mathematical Society, vol. 338 (1993), no. 2, pp. 587–598.
[14] Jan, Krajíček, Lower bounds to the size of constant-depth propositional proofs The Journal of Symbolic Logic, vol. 59 (1994), no. 1, pp. 73–86.
[15] Jan, Krajíček, Bounded Arithmetic, Propositional Logic, and Complexity Theory, Cambridge University Press, Cambridge, 1995.
[16] Jan, Krajíček, Pavel Pudlák, and Gaisi, Takeuti, Bounded arithmetic and the polynomial hierarchy Annals of Pure and Applied Logic, vol. 52 (1991), no. 1-2, pp. 143–153.
[17] Daniel, Leivant, Substructural termination proofs and feasibility certification Proceedings of the 3rd Workshop on Implicit Computational Complexity (Aarhus), 2001, pp. 75–91.
[18] Jeff B., Paris and Alex J., Wilkie, Counting problems in bounded arithmetic Methods in Mathematical Logic (Caracas, 1983) (Carlos Augusto di Prisco, editor), Lecture Notes in Mathematics, vol. 1130, Springer, Berlin, 1985, pp. 317–340.
[19] Wolfram, Pohlers, Proof Theory: An introduction, Lecture Notes in Mathematics, vol. 1407, Springer-Verlag, Berlin, 1989.
[20] Chris, Pollett, Structure and definability in general bounded arithmetic theories Annals of Pure and Applied Logic, vol. 100 (1999), no. 1-3, pp. 189–245.
[21] Gaisi, Takeuti, RSUV isomorphisms Arithmetic, Proof Theory, and Computational Complexity (Prague, 1991) (P., Clote and J., Krajíček, editors), Oxford Logic Guides, vol. 23, Oxford Univ. Press, New York, 1993, pp. 364–386.
[22] Andrew C., Yao, Separating the polynomial-time hierarchy by oracles Proc. 26th Ann. IEEE Symp. on Foundations of Computer Science (Robert E., Tarjan, editor), 1985, pp. 1–10.
[23] Domenico, Zambella, Notes on polynomially bounded arithmetic The Journal of Symbolic Logic, vol. 61 (1996), no. 3, pp. 942–966.
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