AGENTIC-SYSTEMSMay 25, 20261 min read7 views

Inductive Deductive Synthesis: Enabling AI to Generate Formally Verified Systems

Researchers have introduced Inductive Deductive Synthesis (IDS), a novel approach that enables AI to co-synthesize code and formal proofs for complex distributed systems. Operating 200x faster than human experts, IDS marks a significant milestone in generating formally verified, bug-free software.

Computer Science > Artificial Intelligence

Title:Inductive Deductive Synthesis: Enabling AI to Generate Formally Verified Systems

View PDF HTML (experimental)Abstract:AI agents increasingly excel at generating, testing, and refining code. However, they fall short on tasks requiring formal guarantees of full coverage that testing alone cannot provide. Distributed systems are a prime example: properties such as consistency between reads and writes must hold under every possible interleaving of events. Mechanized formal verification can guarantee such correctness, but typically demands months to years of expert effort. As evidence, even SOTA coding agents (Codex with GPT-5.4 and Claude Code with Opus 4.6) succeed on only 2/7 distributed key-value-store specifications. In this paper, we present the first effective approach to addressing this gap, Inductive Deductive Synthesis (IDS), which jointly and incrementally synthesizes implementation and proof, and learns from failed attempts to systematically try promising strategies. Built as an agentic LLM system, IDS achieves 7/7 in about 6.8 hours and $106 per spec on average, roughly 200x faster than expert effort and 17% cheaper than SOTA agents. IDS further incorporates performance feedback into the same loop, yielding implementations up to 3x faster than published verified systems.

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