On the Impossibility of Perfect Security in a Single Computational Space: A Computability-Theoretic Clarification

Attack is computation.Defense is the prevention of computation.Therefore, defense is NOT computation.Thus, no perfect security algorithm can exist within a single computational space. This paper formally organizes this self-evident truth using standard computability theory. We formalize the asymmetry between attack and defense in computational systems. Attack corresponds to computational reachability of forbidden states, which is semi-decidable. Perfect defense corresponds to universal non-reachability, which is generally not decidable for Turing-complete systems. Using reductions from the Halting Problem and implications of Rice’s Theorem, we show that universal algorithmic verification of perfect security cannot exist within a single computational domain. This result unifies known impossibility results including virus detection limits, vulnerability analysis limits, and formal verification limits, under a computability-theoretic framework. The result is not a limitation of current tools or engineering practice, but a fundamental structural property of computation itself.