In Arora's paper, he wrote,
Papadimitriou and Yannakakis also noted that the classical style of reduction (Cook-Levin-Karp [41, 99, 85]) relies on representing a computational history by a combinatorial problem. A computational history is a very non-robust object, since even changing a bit in it can affect its correctness. This nonrobustness lay at the root of the difficulty in proving inapproximability results.
What does he mean by this statement? In particular: what does it mean by 'computational history', and 'representing a computational history by a combinatorial problem'?
I conjecture that: [it is] a very non-robust object, he means that computation could make many many errors. So, in the last statement in the paragraph, maybe he means nonrobustness [the ability to make many errors] lay at the root of the difficulty in proving inapproximability.
Could someone tell me how nonrobustness exists in Karp/Levin reduction?