The Limits of Mathematics
نویسنده
چکیده
In a remarkable development, I have constructed a new definition for a self-delimiting universal Turing machine (UTM) that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory (AIT), which is the theory of the size in bits of programs for self-delimiting UTM’s. Previously, AIT had an abstract mathematical quality. Now it is possible to write down executable programs that embody the constructions in the proofs of theorems. So AIT goes from dealing with remote idealized mythical objects to being a theory about practical down-to-earth gadgets that one can actually play with and use. This new self-delimiting UTM is implemented via software written in a new version of LISP that I invented especially for this purpose. This LISP was designed by writing an interpreter for it in Mathematica that was then translated into C. I have tested this software by running it on IBM RS/6000 workstations with the AIX version of UNIX.
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عنوان ژورنال:
- J. UCS
دوره 2 شماره
صفحات -
تاریخ انتشار 1996