Graph databases are increasingly queried through natural language, yet every existing benchmark evaluates isolated single-turn queries rather than the multi-turn sessions through which analysts actually work. We introduce CypherTurn, the first benchmark for conversational Text-to-Cypher evaluation, comprising 721 sessions and 5,927 turns across 7 knowledge graphs and 13 conversational phenomena. We evaluate 15 models under a guided oracle protocol and a fully autonomous agentic protocol, yielding four findings. First, the best model reaches only 64.7% execution accuracy, and session-level correctness remains below 5%. Second, despite strong overall rank correlation, frontier models exhibit a consequential reordering of the top of the leaderboard under autonomous operation, a phenomenon we term the Autonomy Divergence, which reveals error-management as a partially independent capability from raw generation skill. Third, scaling action budgets from ×3 to ×10 fails to close the autonomy gap, as frontier models self-limit to approximately two actions per turn regardless of available budget. Fourth, single-turn Cypher fine-tuning degrades multi-turn instruction following, while architecture-appropriate specialization outperforms several frontier models. These results establish CypherTurn as an open challenge for conversational graph database reasoning. Code and data are available at https://github.com/BarryQ/CypherTurn.

Recent text-to-SQL models have achieved strong performance, but their effectiveness remains largely confined to SQLite due to dataset limitations. However, real-world applications require SQL generation across multiple dialects with varying syntax and specialized features, which remains a challenge for current models. The main obstacle in building a dialect-aware model lies in acquiring high-quality dialect-specific data. Data generated purely through static prompting—without validating SQLs via execution—tends to be noisy and unreliable. Moreover, the lack of real execution environments in the training loop prevents models from grounding their predictions in executable semantics, limiting generalization despite surface-level improvements from data filtering. This work introduces ExeSQL, a text-to-SQL framework with execution-driven, agentic bootstrapping. The method consists of iterative query generation, execution-based filtering (e.g., rejection sampling), and preference-based training, enabling the model to adapt to new SQL dialects through verifiable, feedback-guided learning. Experiments show that ExeSQL bridges the dialect gap in text-to-SQL, achieving average improvements of 15.2%, 10.38%, and 4.49% over GPT-4o on PostgreSQL, MySQL, and Oracle, respectively, across multiple datasets of varying difficulty.