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I've never used this syntax before, but if it is compilable, it must mean c is the exclusive nor of a and b. It is using the equality operator to check if a is the same logical level as b. I would write it using the Verilog XNOR operator, since it is more intuitive to me:
assign c = a ~^ b;
Good point, I had made an assumption that a and b are each 1 bit, based on incomplete context. For the case where a and b are vectors of equal and arbitrary size you could get the desired behavior by ANDing all the bits from my previous equation as follows:
assign c = &(a ~^ b);
But that seems unnecessarily confusing.
I ran the original syntax (a == b) through Cadence's HAL lint checker, and theres no problem with it at all, so perhaps it is the most ideal solution.