Friday, February 13

A P-Complete Problem

We discussed and presented the reduction that showed that the problem Circuit Value is P-complete.  The technique was similar to the original proof that SAT is NP-complete.  The idea is that we needed to find a log-space Turing machine (algorithm) that reduced any problem in P to Circuit Value.  Any problem in P has a deterministic Turing machine M that runs in polynomial time. For any input, x, to M we can express the computation of M on x with a computation table.  This table can be encoded in binary, and the binary values can be cleverly input to a circuit at each level that produce the binary values for the next level in the table.  The circuit is so constructed that its output is "true" iff the original M accepts x.  Thus, we have a reduction.  Since the reduction can be done in log space, it follows that circuit value is P-complete.