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Published equation contexts

accept⁡(s′)=1 ⁣[⋀i=1mvi(s′)=1]⋅u(s′)\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s')

Why this formula appears here

Suppose verification functions v1v_1,…\dots,vmv_m each observe a projection of changed state s' . Acceptance is accept⁡(s′)=1 ⁣[⋀i=1mvi(s′)=1]⋅u(s′)\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s'). where u(s') represents required human or institutional authorization. Even if every viv_i passes, the false-accept probability is not zero because the conjunction covers only encoded properties. Correlated checks can repeat the same blind spot.

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Published contexts (1)

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accept⁡(s′)=1 ⁣[⋀i=1mvi(s′)=1]⋅u(s′),\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s'),

Equation 42 · AI Agents & Systems

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Suppose verification functions v1v_1,…\dots,vmv_m each observe a projection of changed state s' . Acceptance is accept⁡(s′)=1 ⁣[⋀i=1mvi(s′)=1]⋅u(s′)\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s'). where u(s') represents required human or institutional authorization. Even if every viv_i passes, the false-accept probability is not zero because the conjunction covers only encoded properties. Correlated checks can repeat the same blind spot.

Meanings in this article

  • uu: required human or institutional authorization.
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