A Quantifier-Alternation Calculus for Robust Monitor Synthesis Parametric Arithmetical-Hierarchy Completeness for Double-Bind Machines
Year: 2025
Type: article
Abstract: This paper introduces a novel computational model, the Double Bind Machine (DBM),to formalize the logic of paradoxical communication, inspired by Gregory Bateson’s conceptof the ”double bind.” The DBM is a variant of the Turing machine whose transition rulesare contingent upon competing ”interpretive frames.” A state of logical contradiction isformally defined as a configuration where different frames prescribe incompatible actions.Upon detecting such a contradiction, the machine enters a non-recoverable trap state. Wedefine the Escape Problem: whether a given DBM can reach an accepting state on someinput without entering this trap state. The central result is a rigorous proof that the EscapeProblem is undecidable. This is established by constructing a detailed many-one reductionfrom the Halting Problem for Turing machines (HT M ). This result formally demonstratesthe impossibility of algorithmically determining if a non-paradoxical computational pathexists within such systems. We situate the DBM within a unified framework, contrasting itsuncomputability with the tractability of the Double Boon Machine and the computationalhardness of the Bateson One-Way Function.
Author: Fathi, Kevin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6912083946
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