Persistent State Machine: A Formal Computational Paradigm for High-Sparsity LLM Attention Acceleration (Version 3.3) ABSTRACT: The von Neumann memory wall—the bandwidth and energy gap between computation and data storage—has become the dominant bottleneck of Large Language Model (LLM) inference. In autoregressive decoding, every generated token requires re-streaming the entire Key-Value (KV) cache across DRAM, consuming energy four to five orders of magnitude above the arithmetic cost. This paper introduces the Persistent State Machine (PSM), a formal computational paradigm where computation is broadcast as instructions to stationary in-memory cells that evaluate state transitions locally. We define PSM as a mathematical 7-tuple, prove its representation equivalence and exponential reduction in explicit lookup-table implementation complexity over Deterministic Finite Automata (DFA), and establish its formal equivalence to Deterministic Linear Bounded Automata (DLBA) under linear bounded memory constraint N = O(n), characterizing the deterministic space complexity class DSPACE(O(n)). We present the Active State-machine Memory Architecture (ASMA), a proposed silicon architecture implementing PSM for LLM KV-cache attention. Under the analytical model and operating assumptions described in Section 4 (INT4 precision, N=4,096 sequence length basis), ASMA is projected to reduce system bus traffic by up to 99.47% and net step energy by 99.0% (Horowitz 45 nm CMOS energy model basis) against GPU baselines. Note: All quantitative results in this paper are derived from mathematical proofs, arithmetic calculations, analytical energy models (Horowitz 2014), and Python software simulations. No physical silicon fabrication, FPGA synthesis, or gate-level timing analysis has been performed at the time of this publication. Synthesizable Verilog-2001 RTL source code is provided as a reference design. --- Japanese Patent Application No. 2026-177318 (Patent Pending).