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τ=(s0,o0,a0,s1,…,aT−1,sT)\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T)

Why this formula appears here

Let a task generate a trajectory τ=(s0,o0,a0,s1,…,aT−1,sT)\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T). where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is

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aT−1a_{T-1}

Symbol a_T-1

aTa_T-1 is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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τ=(s0,o0,a0,s1,…,aT−1,sT),\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T),

Equation 1 · AI Agents & Systems

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

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

Let a task generate a trajectory τ=(s0,o0,a0,s1,…,aT−1,sT)\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T). where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is

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