Τρίτη, 23 Σεπτεμβρίου 2008

Hypercomputation Book

I am really happy to announce that my book on Hypercomputation has been published by Springer. Hypercomputation is a new discipline that emerged from the ascertainment that the Church-Turing Thesis (CTT) cannot be possible true. Roughly, the CTT is about what can be computed with any real or conceptual computing device. In particular, if some function is computable, then it is definitely computable by a Turing mchine, that is, Turing's archetypal conceptual computing device. Hypercomputation, asserts that functions and numbers that cannot be computed by a Turing machine, can be computed by other more powerful computing devices. The description of such machines and their computational power is the subject of this book. In particular, the book describes the various approaches to hypercomputation in nine chapters
  • Introduction
  • On the Church–Turing Thesis
  • Early Hypercomputers
  • Infinite-Time Turing Machines
  • Interactive Computing
  • Hyperminds
  • Computing Real Numbers
  • Relativistic and Quantum Hypercomputation
  • Natural Computation and Hypercomputation
There are also three appendices that briefly describe some important issues:
  • The P = NP Hypothesis
  • Intractability and Hypercomputation
  • Socioeconomic Implications

A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...