Beyond Godel

Abstract

In this paper, we start by defining the basic predicate systems used by Gödel in his logical constructions for the creation of a system of computable mathematics. We demonstrate how each of these predicates and the primitive recursive functions can be mapped directly into bitcoin script operations. This is then extended to explore the dual stack 2PDA construction within bitcoin. In this paper we use this extension to demonstrate how the integration of these functions across a dual stack push down automata (2PDA) allows us to create a system that is equivalent to a Turing machine and which can hence handle all grammatical constructs that may be processed within a Turing machine. The function and operation of the bitcoin operational codes and the construction of the stacks leads to different operational conditions than a standard Turing machine, however, it is also noted how this differs from a standard modern registered machine in operation. Ignoring stack limitations we can then see that any computable function may be integrated into operation and solution within bitcoin scripts.

Keywords: Bitcoin, Turing Machines, Unrolled recursion