Recognition Science: The Complete Theory of Physical Computation
Recognition Physics Institute
Summary
Recognition Science (RS) separates internal evolution (computation) from external observation (recognition). The paper presents a reversible cellular automaton realizing this separation and a uniform CA→TM compilation with explicit bounds. Under the stated RS–CA hypothesis (fixed rule, polynomial volume, CA time $O(n^{1/3}\log n)$, linear decoder), the compilation yields a polynomial‑time TM decider for 3SAT (conditional). A seeded, randomized encoder variant compiles to RP/ZPP‑type TMs with one‑sided/zero‑error guarantees (also conditional); remaining blockers are listed and model‑level intuition is separated from classical consequences.
Abstract
We introduce Recognition Science (RS), a framework that separates internal evolution (computation) from external observation (recognition). We present a reversible cellular automaton (CA) construction that realizes this separation and formalize a uniform CA→TM compilation theorem with an explicit time bound. Under an RS–CA hypothesis (one fixed local rule, polynomial‑volume layouts, CA time $O(n^{1/3}\log n)$, linear‑time decoder), the compilation yields a polynomial‑time TM decider for 3SAT (conditional). We also give a randomized, seeded‑encoder variant (Valiant–Vazirani style) that compiles to RP/ZPP‑type TMs with one‑sided/zero‑error guarantees (also conditional). We clearly separate model‑level intuition from classical consequences and list the remaining blockers. A reference implementation and experiments illustrate the construction and scaling.
Key Points
- Dual complexity parameters: Every problem has computation complexity $T_c$ and recognition complexity $T_r$.
- Fundamental separation: For SAT, $T_c = O(n^{1/3}\log n)$ while $T_r = \Omega(n)$ under the construction.
- Uniform CA→TM compilation: Fixed‑rule CA with linear‑time decoder compiles to a polynomial‑time TM (conditional for 3SAT).
- Randomized variants: Seeded‑encoder version compiles to RP/ZPP‑type TMs with one‑sided/zero‑error guarantees (conditional).
- Constructive demonstration: Reversible CA and reference implementation with experiments illustrating scaling.