A Non-Turing Computer Architecture for Artificial Intelligence with Dynamic Rule Learning and Generalization Abilities and Its Halting Problem

Since the beginning of modern computer history, the Turing machine has been a dominant architecture for most computational devices, which consists of three essential components: an infinite tape for input, a read/write head, and finite control. In this structure, what the head can read (i.e., binary digits and symbols) is the same as what it has written/outputted. This is actually different from the ways in which humans think or do thought/tool experiments, where inputs can be abstract symbols while outputs can be images. Compared with this architecture, the proposed architecture uses two different types of heads and tapes, one processing specific multimodal information, including images and texts, and the other processing traditional binary digits and symbols that can perform calculation, rigid concept definition, and rigid formal logic. The mapping rules among the abstract symbols and the specific images/texts can be realized by neural networks with a high accuracy rate. Logical reasoning is thus performed through the transfer of mapping rules. The statistical decidability of the Halting Problem with an imperceptibly small error rate in reasoning steps is established for this type of machine. As an example, this paper presents how the new computer architecture (what we call “Ren machine” for simplicity here) autonomously learns a distributive property/rule of multiplication in the specific domain and further uses the rule to generate a general method (mixed in both the abstract domain and the specific domain) to compute the multiplication of any positive integers based on images/texts. The machine’s strong reasoning ability is also corroborated in proving a theorem in Plane Geometry. Moreover, a robotic architecture based on Ren machine is proposed to address the challenges faced by the Vision-Language-Action (VLA) models in unsound reasoning ability and high computational cost.