On Repetitive Finite Automata with Translucent Words

2025-07-21

AI Summary

This paper investigates the language recognition capabilities of finite automata with transparent words under the “repetition” mechanism (DFAwtw/NFAwtw). To overcome the limitation of conventional models—which halt immediately upon reading the right sentinel—the repetition mechanism permits additional state transitions after encountering the right-end marker, thereby extending the computation. Theoretically, this mechanism substantially enhances expressive power: even the deterministic variant (DFAwtw) recognizes non-semilinear languages, surpassing both classical DFAs and standard transparent-word automata. Moreover, we establish an exponential state complexity gap between NFAwtw and DFAwtw; the language class of NFAwtw strictly contains all semilinear languages yet excludes all context-free languages. This work provides the first systematic characterization of how the repetition mechanism fundamentally augments the computational power of finite automata.

Technology Category

• Natural Language Processing: Lexical Semantics and Morphology
• Machine Learning: Transparent, Interpretable, Explainable ML
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting or rejecting, but it may change into another state and continue with its computation. We establish that a repetitive DFAwtw already accepts a language that is not even semi-linear, which shows that the property of being repetitive increases the expressive capacity of the DFAwtw and the NFAwtw considerably.

Problem

• Study repetitive variants of finite automata with translucent words
• Analyze non-halting behavior in repetitive NFAwtw upon sentinel
• Demonstrate increased expressive capacity of repetitive DFAwtw

Innovation

• Repetitive finite automata with translucent words
• Non-halting computation after right sentinel
• Increased expressive capacity for automata