Compare and swap has a consensus number of 2. A consensus number is the maximum number of processes for which the object can solve a simple consensus problem. It is impossible to construct a wait-free implementation of an object with consensus number n from an object with a lower consensus number.
In other words, test-and-set is weaker than transactions or Paxos for &gt;2 concurrent clients.<p><a href="http:&#x2F;&#x2F;cs.brown.edu&#x2F;~mph&#x2F;Herlihy91&#x2F;p124-herlihy.pdf" rel="nofollow">http:&#x2F;&#x2F;cs.brown.edu&#x2F;~mph&#x2F;Herlihy91&#x2F;p124-herlihy.pdf</a>