Cluster automata

TL;DR

The paper introduces Clustered Moore Automata (CMA), a hierarchical, multi-timescale extension of Moore transducers in which inner CMA operate on faster timescales than outer CMA, bounded by an Artinian constraint. It provides formal definitions (including a memory architecture with per-layer limits $m=10^4$, $s=2^8$, $o<8$, $i<m$) and proves that any CMA timescale is bisimilar to one of five discrete structures $Z,N,P,L,C$, establishing a finite taxonomy of temporal behaviors. The authors detail both the naive, discrete-time worldview and linguistic applications, showing how CMA can model tense, aspect, causation, bound morphemes, and island parsing, with concrete examples such as Exchange and Gravity. They outline a grammar-building approach that leverages CMA for lexical activation and graph-based pattern assembly, and discuss potential relevance to modern NLP systems and LLM-inspired architectures, while acknowledging memory and I/O limitations and future research directions. Overall, CMA offers a rigorous, multi-scale, finite-state framework for modeling temporal structure and linguistic cognition across scales, with practical implications for language understanding and computation.

Abstract

We introduce a new class of clustered Moore automata (CMA), investigate their temporal behavior, and describe some applications.

Figures (2)

• Figure 1: State diagram and transition matrix of $\mathcal{S}_2^1$.
• Figure 2: State diagram of the abstract synapse $\mathcal{R}$