The removal of from some undecidable problems involving elementary functions
暂无分享,去创建一个
We show that in the ring generated by the integers and the functions x; sin x(n) and sin(x . sin x(n)) (n = 1, 2,...) defined on R it is undecidable whether or not a function has a positive value or has a root. We also prove that the existential theory of the exponential field C is undecidable.
[1] Paul S. Wang. The Undecidability of the Existence of Zeros of Real Elementary Functions , 1974, JACM.
[2] Daniel Richardson,et al. Some undecidable problems involving elementary functions of a real variable , 1969, Journal of Symbolic Logic.
[3] Lauwerens Kuipers,et al. Uniform distribution of sequences , 1974 .
[4] B. F. Caviness. On Canonical Forms and Simplification , 1970, JACM.