A normal form for restricted exponential functions

Pierpaolo Degano; Patrizia Gianni

doi:10.1051/ita/1989230202171

All issues

Volume 23 / No 2 (1989)

RAIRO-Theor. Inf. Appl., 23 2 (1989) 217-231

References

Free Access

Issue		RAIRO-Theor. Inf. Appl. Volume 23, Number 2, 1989


Page(s)		217 - 231
DOI		https://doi.org/10.1051/ita/1989230202171
Published online		01 February 2017

1. G. H. HARDY, Orders of infinity, Cambridge Tracts in Math. Phys., 12, Cambridge University Press 1910, Reprint Hafner, New York. [Zbl: 41.0303.01] [JFM: 41.0303.01] [Google Scholar]
2. C. W. HENSON and L. A. RUBEL, Some Applications of Nevalinna Theory to Mathematical Logic: Identities of Exponential Functions, Trans. of the American Math. Soc., Vol. 282, No. 1, 1984, pp. 1-32. [MR: 728700] [Zbl: 0533.03015] [Google Scholar]
3. G. HUET and D. C. OPPEN, Equations and Rewrite Rules: A Survey. In: Formal Languages Theory: Perspectives and Open Problems, R. BOOK Ed., Academic Press, New York, 1980, pp. 349-405. [Google Scholar]
4. D. LANKFORD, On Proving Term Rewriting Systems are Noetherian, Rep. MTP-3, Louisiana Tech. Univ., 1979. [Google Scholar]
5. H. LEVITZ, An Ordered Set of Arithmetic Functions Representing the Least ε-Number, Z. Math. Logik Grundlag. Math., Vol. 21, 1975, pp. 115-120. [MR: 371627] [Zbl: 0325.04002] [Google Scholar]
6. A. MACINTYRE, The Laws of Exponentiation. In: Model Theory and Arithmetic, C. BERLINE, K. MCALOON and J.-P. RESSAYRE Eds., Lecture Notes in Mathematics, No. 890, Springer-Verlag, Berlin, 1981, pp. 185-197. [MR: 645003] [Zbl: 0503.08008] [Google Scholar]
7. C. MARTIN, Equational Theories of Natural Numbers and Transfinite Ordinals, Ph. D. Thesis, Univ. of California, Berkley, 1973. [Google Scholar]
8. G. E. PETERSON and M. E. STICKEL, Complete Sets of Reductions for Some Equational Theories, J. of the A.C.M., Vol. 28, 1981, pp. 233-264. [MR: 612079] [Zbl: 0479.68092] [Google Scholar]
9. A. TARSKI, Equational Logic and Equational Theories of Algebras. In: Contributions to Mathematical Logic, H. A. SCHMIDT, K. SHUTTE and H. J. THIELE Eds., North-Holland, Amsterdam, 1968, pp. 275-288. [MR: 237410] [Zbl: 0209.01402] [Google Scholar]
10. A. J. WILKIE, On Exponentiation - A Solution to Tarskfs High School Algebra Problem. Unpublished Manuscript, quoted in Assoc. of Automated Reasoning Newsletter, Vol. 3, 1984, p. 6. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

[1] 1. G. H. HARDY, Orders of infinity, Cambridge Tracts in Math. Phys., 12, Cambridge University Press 1910, Reprint Hafner, New York. [Zbl: 41.0303.01] [JFM: 41.0303.01] [Google Scholar]

[2] 2. C. W. HENSON and L. A. RUBEL, Some Applications of Nevalinna Theory to Mathematical Logic: Identities of Exponential Functions, Trans. of the American Math. Soc., Vol. 282, No. 1, 1984, pp. 1-32. [MR: 728700] [Zbl: 0533.03015] [Google Scholar]

[3] 3. G. HUET and D. C. OPPEN, Equations and Rewrite Rules: A Survey. In: Formal Languages Theory: Perspectives and Open Problems, R. BOOK Ed., Academic Press, New York, 1980, pp. 349-405. [Google Scholar]

[4] 4. D. LANKFORD, On Proving Term Rewriting Systems are Noetherian, Rep. MTP-3, Louisiana Tech. Univ., 1979. [Google Scholar]

[5] 5. H. LEVITZ, An Ordered Set of Arithmetic Functions Representing the Least ε-Number, Z. Math. Logik Grundlag. Math., Vol. 21, 1975, pp. 115-120. [MR: 371627] [Zbl: 0325.04002] [Google Scholar]

[6] 6. A. MACINTYRE, The Laws of Exponentiation. In: Model Theory and Arithmetic, C. BERLINE, K. MCALOON and J.-P. RESSAYRE Eds., Lecture Notes in Mathematics, No. 890, Springer-Verlag, Berlin, 1981, pp. 185-197. [MR: 645003] [Zbl: 0503.08008] [Google Scholar]

[7] 7. C. MARTIN, Equational Theories of Natural Numbers and Transfinite Ordinals, Ph. D. Thesis, Univ. of California, Berkley, 1973. [Google Scholar]

[8] 8. G. E. PETERSON and M. E. STICKEL, Complete Sets of Reductions for Some Equational Theories, J. of the A.C.M., Vol. 28, 1981, pp. 233-264. [MR: 612079] [Zbl: 0479.68092] [Google Scholar]

[9] 9. A. TARSKI, Equational Logic and Equational Theories of Algebras. In: Contributions to Mathematical Logic, H. A. SCHMIDT, K. SHUTTE and H. J. THIELE Eds., North-Holland, Amsterdam, 1968, pp. 275-288. [MR: 237410] [Zbl: 0209.01402] [Google Scholar]

[10] 10. A. J. WILKIE, On Exponentiation - A Solution to Tarskfs High School Algebra Problem. Unpublished Manuscript, quoted in Assoc. of Automated Reasoning Newsletter, Vol. 3, 1984, p. 6. [Google Scholar]