Carrying proofs forward.
Verification produces evidence and proof structures that can remain useful for later decisions. We study the conditions under which this accumulated work can be reused, focusing on repeated proof construction across queries and duplicated evidence acquisition across tasks.
2,187→57
Partial observation histories → Proof keys
In the studied seven-query instance, 2,187 partial observation histories were organized into 57 proof keys.
Relationships between queries can allow different observation histories to use a common proof representation. We derive conditions for this sharing within structured execution models and compare the resulting representations with the original models to check that the required semantics are preserved.
Reused structures are checked against the inputs and conditions to which they apply. The checks cover each requested history and detect omitted requests, retaining a traceable connection between the evidence and the conclusion.
Evidence across tasks
When tasks share observation sources whose fault status persists across the group, evidence from one task can inform another. For the studied task families, we determine the exact amount of additional evidence required for joint verification.
Once the base evidence has been obtained, joint verification can reduce additional acquisition cost compared with verifying each task using only its own evidence. Together, proof sharing and joint use of evidence make accumulated verification work useful for subsequent decisions.
When evidence need not be acquired again.
Even when an update invalidates one proof, another combination of stored evidence may remain available. Under specified fault, update, and execution conditions, we established necessary and sufficient conditions for completing execution without reacquiring evidence, by switching among evidence already acquired.
For a specified family of evidence configurations, we also determined the exact worst-case continuation cost, including failed checks and additional acquisition. We distinguish the initial cost of acquiring evidence from the costs required afterward, and establish a lower bound across the entire declared strategy class together with a procedure that attains it.