A probabilistic algorithm for updating files over a communication link

Consider two people, P and Q, connected with a bidirectional communication link. Let P have a binary string 2 and let Q have y, The string y can be obtained from x by a small number k of editing operations: inserting/deleting a bit and copying/moving/deleting a block (substring). Our problem is to communicate the string y to P using a small number of bits in both directions. We present a probabilistic algorithm for that task aud prove that for any Z, y and E > 0 the algorithm communicates y (the string that Q has) to P with probability 1 E using poly(log 1~1, log ]y], loge-l, k) bits. The running time is poly(]z], ]y],log~-l).