... size of at least 2 m /2+ 1 to express in the OR-of-XOR language.It is also possible to define a language of XOR-of-OR bids, and even a lan-guage allowing arbitrary nesting of OR and XOR statements ... but not the other, and vice-versa. Third, the OR*language is strictly more expressive than both the OR-of-XOR and XOR-of-ORlanguages: it can efficiently simulate both languages, and succinctly expresssome ... Westated an atomic bid above when we wanted to bid on the couch, the TV, andthe VCR for $100.Of course, many simple bids cannot be expressed as an atomic bid; for ex-ample, it is easy to verify...