Equivalence Is In The Eye Of The Beholder

In a provocative paper “Processes are in the Eye of the Beholder” in the same issue of TCS (pages 333-351), Lamport points out “the insubstantiality of processes” by proving the equivalence of two different decompositions of the same intuitive algorithm. More exactly, each of the two distributed algorithms is described by a formula in Lamport’s favorite temporal logic and then the two formulas are proved equivalent. We point out that the equivalence of algorithms is itself in the eye of the beholder. In this connection, we analyse in what sense the two distributed algorithms are and are not equivalent. Our equivalence proof is direct and does not require formalizing algorithms as logic formulas.