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Race Condition Analysis

The analysis of timing dependencies in sequential circuits where the output depends on the order of signal arrival, often mitigated by synchronous clocking and proper clock gating.
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The statement of the theorem

A race condition occurs when the circuit output depends on the non-deterministic order of signal arrival. Formally, if the circuit behavior OO is modeled by a set of differential equations V˙=g(V,t)\dot{\mathbf{V}} = g(\mathbf{V}, t), a race condition implies that the solution V(t)\mathbf{V}(t) is not unique or stable with respect to the timing delays τi\tau_i. Mitigation requires ensuring that all state updates are synchronized to a common clock edge, enforcing a deterministic transition function δ\delta.