In large SoCs, connecting IP blocks is a major source of bugs (wrong wire, swapped bits). Formal connectivity checks prove that the top-level wiring matches the specification without needing test vectors.
The toolkit must include techniques for abstraction. Replace a complex multiplier with a "uninterpreted function." Remove non-critical datapaths to reduce state space. The art of formal is knowing what to abstract away.
As designs shrink, corner cases—those obscure, hard-to-reach states where bugs often hide—become increasingly difficult to reach with constrained-random stimuli. A bug that exists in a logic path that is only exercised once every million cycles may never be uncovered in a standard regression suite. In the context of modern VLSI, missing a corner case can result in a "respins"—a re-fabrication of the silicon that costs millions of dollars and months of delays. This is where the search for a becomes a strategic priority for engineering teams seeking a deterministic solution.