Using PVS to validate the inverse trigonometric functions of an exact arithmetic

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2991, Issue , 2004, Pages 259-273

  Lester, David ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

VERIFICATION;

CAUCHY SEQUENCE; EXACT ARITHMETIC; TRIGONOMETRIC FUNCTIONS;

FUNCTIONS;

EID: 35048864932     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24738-8_16     Document Type: Article

References (17)

1. M. Abramovitz, I.A. Stegun, Handbook of Mathematical Functions (Ninth Edition), Dover Publications, New York, 1972.
2. E.W. Dijkstra, A Discipline of Programming, Prentice-Hall, Englewood Cliffs, 1976.
3. C.A.R. Hoare, An Axiomatic Basis for Computer Programming. Communications of the ACM, 12(10):576-580, October 1969.
4. K.-I. Ko, On the definitions of some complexity classes of real numbers, Math. Systems Theory 16 (1983) 95-109.
5. V. A. Lee Jr., H.-J. Boehm, Optimizing programs over the constructive reals, in: Proceedings of the ACM SIGPLAN'90 conference on Programming Language design and implementation, 1990, pp. 102-111.
6. D. R. Lester, P. Gowland, Using PVS to validate the algorithms of an exact arithmetic, in: TCS 291, 2003, pp 203-218.
7. V. Ménissier-Morain, Arithmétique exacte, Ph.D. thesis, L'Université Paris VII (Dec. 1994).
8. A. Mostowski, On computable sequences, Fundamenta Mathematicae 44 (1957) 37-51.
9. N. T. Müller, Subpolynomial complexity classes of real functions and real numbers, in: L. Kott (Ed.), Proceedings of the 13th International Colloquium on Automata, Languages, and Programming, Vol. 226 of Lecture Notes in Computer Science, Springer, Berlin, 1986, pp. 284-293.
10. N. T. Müller, Towards a real Real RAM: a prototype using C++, in: K.-I. Ko, N. Müller, K. Weihrauch (Eds.), Computability and Complexity in Analysis, Universität Trier, 1996, pp. 59-66, second CCA Workshop, Trier, August 22-23, 1996.
11. N. T. Müller, Implementing limits in an interactive RealRAM, in: J.-M. Chesneaux, F. Jézéquel, J.-L. Lamotte, J. Vignes (Eds.), Third Real Numbers and Computers Conference, Université Pierre et Marie Curie, Paris, 1998, pp. 59-66, paris, France, April 27-29, 1998.
12. S. Owre, N. Shaker, J.M Rushby, D.W.J. Stringer-Calvert, PVS System Guide, Computer Science Laboratory, SRI International, Menlo Park, CA, September 1999. Available from http://pvs.csl.sri.com.
13. M. B. Pour-El, J. I. Richards, Computability in Analysis and Physics, Perspectives in Mathematical Logic, Springer, Berlin, 1989.
14. H. Rice, Recursive real numbers, Proc. Amer. Math. Soc. 5 (1954) 784-791.
15. R. Robinson, Review of "Peter, R., Rekursive Funktionen", The Journal of Symbolic Logic 16 (1951) 280-282.
16. E. Specker, Nicht konstruktiv beweisbare Sätze der Analysis, The Journal of Symbolic Logic 14 (3) (1949) 145-158.
17. K. Weihrauch, Computability, Vol. 9 of EATCS Monographs on Theoretical Computer Science, Springer, Berlin, 1987.