This framework examines representational preconditions for computability, suggesting a new approach to problem-solving.
This work introduces the Hierarchical Representational Machine (HRM), a formal framework for analyzing the representational preconditions of computability. While classical computability and complexity theory focus on algorithmic efficiency over fixed symbolic encodings, the HRM examines whether a problem is representationally well-posed for a given computational system. The framework stratifies representational resources into four layers: Structured Input Space (L1), Equivalence and Measurement (L2), Formal Symbolic Representation (L3), and Admissibility Constraints (L4). Grounded in Type-2 Theory of Effectivity and related formalisms, the HRM shows that representational hierarchy is orthogonal to, yet as fundamental as, time and space complexity in determining problem solvability.
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Chainarong Amornbunchornvej (2026) studied this question.
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