Abstract

Large language models (LLMs) have demonstrated strong performance on formal language tasks, yet whether this reflects genuine symbolic reasoning or pattern matching on familiar constructions remains unclear. We introduce a benchmark for deterministic finite automata (DFA) construction from regular languages, comprising factual knowledge questions, seen construction problems from public sources, and two types of unseen problems: hand-crafted instances with multiple interacting constraints and systematically generated problems via Arden’s theorem. Models achieve perfect accuracy on factual questions and 84-90% on seen tasks. However, accuracy drops sharply on unseen problems (by 30-64%), with failures stemming from systematic misinterpretation of language constraints, incorrect handling of Kleene-star semantics, and a failure to preserve global consistency. We evaluate a three-stage hint protocol that enables correction of shallow errors but does not reliably resolve globally inconsistent or structurally flawed automata. Our analysis across multiple prompting strategies (direct, Chain-of-Thought, Tree-of-Thought) reveals that errors persist regardless of prompting approach, exposing a fundamental gap between LLMs’ ability to generate syntactically plausible DFAs and their capacity for semantically correct formal reasoning.