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Informatics pp 251–256Cite as

Computational Complexity and Mathematical Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2000))

Abstract

This paper discusses howthe major computational complexity classes, P, NP and PSPACE, capture different computational properties of mathematical proofs and reveal newq uantitative aspects of mathematics.

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References

  1. O. Goldreich, S. Micali, and A. Widgerson. Proofs that yield nothing but their validity and a methodology of cryptographic protocol design. In IEEE Symposium on Foundations of Computer Science, pages 174–187, 1986.

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  2. S. Goldwasser. Interactive proof systems. In Proceedings of Symposia in Applied Mathematics, pages 108–128. American Mathematical Society, 1989.

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  3. J. Hartmanis, D. Ranjan R. Chang, and P. Rohatyi. On IP = PSPACE and theorems with narrow proofs. EATCS-Bulletin, 41:166–174, 1990.

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  4. C. Lund, L. Fortnow, H. Karlo., and N. Nisan. Algebraic methods for interactive proofs. In Proceedings 31st IEEE Symp. on the Foundations of Computer Science, pages 1–10, 1990.

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  5. A. Shamir. IP = PSPACE. In Proc. 31st IEEE Symp. on the Foundations of Computer Science, pages 11–15, 1990.

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© 2001 Springer-Verlag Berlin Heidelberg

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Hartmanis, J. (2001). Computational Complexity and Mathematical Proofs. In: Wilhelm, R. (eds) Informatics. Lecture Notes in Computer Science, vol 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44577-3_17

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  • DOI: https://doi.org/10.1007/3-540-44577-3_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41635-7

  • Online ISBN: 978-3-540-44577-7

  • eBook Packages: Springer Book Archive

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