Dynamic Register Machine Solving Undecidable Computations
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Solution Overview
Problem
Current computing machines and software applications are unable to solve the Turing Immortality problem and other computational problems effectively, as they are limited by the Church-Turing thesis and lack the capability to dynamically modify their instructions during execution.
Innovation Solution
A Dynamic Register Machine (DRM) is introduced, which can change its program while executing by adding or removing instructions, using a set of seven types of instructions (Constant, Successor, Transfer, Address, Jump, Delete, and Update) to perform computations that traditional Turing machines cannot, such as determining whether a given Turing machine has immortal configurations in a finite number of steps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional Turing machines are used to solve computational problems, then the machine structure remains simple and fixed, but the machine cannot solve the Turing Immortality problem and other undecidable problems
Solution Approach 1:
The patent applies the dynamics principle by transforming the static, fixed program structure of traditional Turing machines into a dynamic structure where instructions can be modified, added, or removed during execution. The Dynamic Register Machine allows the program to change its own structure through self-modifying code, enabling the machine to adapt its computational behavior dynamically to solve previously undecidable problems while maintaining a relatively simple underlying architecture.
2Adaptability or versatility
If the program is fixed during execution as in traditional machines, then the machine is easier to control and implement, but it cannot dynamically modify instructions to solve undecidable problems
Solution Approach 1:
The patent implements the self-service principle through self-modifying code that allows the program to modify its own instructions during execution. The Dynamic Register Machine can add, remove, or alter instructions in its own program sequence without external intervention, enabling the system to automatically adapt its control flow and computational logic to solve problems that require dynamic reconfiguration of the execution pathway.
3Adaptability or versatility
If the machine follows the Church-Turing thesis with fixed instructions, then implementation is straightforward, but it cannot determine immortal configurations of Turing machines
Solution Approach 1:
The patent applies the preliminary action principle by having the Dynamic Register Machine pre-process and analyze the Turing machine configuration before full execution begins. The system performs preliminary setup of registers, initial program configuration, and preparatory computations that enable the subsequent dynamic instruction modification to proceed efficiently, reducing the overall time required to determine immortal configurations compared to attempting direct simulation.
Data Source
AI summary
A computing machine is disclosed having a memory system for storing a collection of execution nodes, a head for reading a sequence of symbols in the execution nodes in the memory system, and writing a sequence of symbols in the memory system. The machine is configured to execute a computation with a collection of pairs of execution nodes. Each pair of execution nodes represents a machine instruction. One execution node in the pair represents input of the machine instruction represented by the execution nodes. Another execution node in the pair represents output of the machine instruction represented by the execution nodes. Each execution node has a state of the machine, a sequence of symbols and a number.