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Which cryptographic tool can be used to prove that a program passes a certain test?

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Let's say I have a smart contract located at an address A, and another smart contract that runs tests on A located at A'. A may contain a reference to this test contract and have a function like runTests that runs A' using the bytecode of A.

My question is: is there a way to prove that A passed the test, so that the test need not be run again? I mean, suppose A stores a variable called passedTest and this is set to true. We would just need to take the contract owner's word for it that the test was passed. But could there be some sort of hash that passedTest could be set to, such that no one could doubt that the test was passed?

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