Andy Melnikov (nponeccop) wrote,
Andy Melnikov
nponeccop

Уравнение, эквивалентное задаче останова

Диофантово уравнение с параметром, решение которого в общем виде эквивалентно задаче останова

Formalisms for Computation: Register Machines, Exponential Diophantine Equations, & Pure LISP

By Gregory. J. Chaitin

we present a method for compiling register machine programs into exponential diophantine equations. In Chapter 3 we present a stripped-down version of pure LISP. And in Chapter 4 we present a register machine interpreter for this LISP, and then compile it into a diophantine equation. The resulting equation, which unfortunately is too large to exhibit here in its entirety, has a solution, and only one, if the binary representation of a LISP expression that halts, i.e., that has a value, is substituted for a distinguished variable in it. It has no solution if the number substituted is the binary representation of a LISP expression without a value.
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