Church’s Problem: Automatic Circuit Synthesis from Input–Output Specifications

Establish an algorithmic procedure that, given a formal specification of the functional relationship between circuit inputs and outputs, automatically designs a circuit that realizes the specified relationship while guaranteeing correctness. This is the classical Church’s Problem in automatic circuit synthesis, which remains unsolved and underpins automated processor chip design.

Background

The paper situates automated processor chip design within the historical context of Church’s Problem, posed in 1957, which asks how to automatically construct circuits from input–output relations. Despite decades of research, including contributions from leading figures in theoretical computer science, this foundational synthesis question remains unresolved.

The authors discuss how modern automated chip design approaches and AI-driven methods address parts of the design pipeline but do not solve the end-to-end synthesis challenge implied by Church’s Problem. This unresolved status motivates QiMeng’s multi-layered approach toward fully automated hardware–software co-design while acknowledging the enduring open nature of the core synthesis question.