I don't understand the motivation for using C1 for CRFs. Using C0, they get an error rate of nearly 100%, so by just saying the opposite of what the CRF using C0 says, you'd get nearly 0% error. However, using C1, you get ~50% error, which the authors claim is optimal. If it's possible to consistently get ~100% error, then it is possible to consistently get ~0% error, so ~50% is not optimal, is it?

I think this paper does a reasonably good job of promoting its new objective function. This sort of objective function has been used in HMM's before, hasn't it? I thought the Viterbi algorithm was an improvement on using this sort of greedy algorithm for HMM evaluation. The motivations for C1, particularly for CRF's, seemed somewhat obscure. I think C1 is a good alternatice objective function, depending on what the actual task to be accomplished is.

For binary problems, 100% of error is as good as 0%, but the example in section 3.2.1 has 4 possible labels.

I too was fairly impressed with the performance of the new objective function. I was a bit disappointed, however, with the explaination of the results and the presentation of the experimental results. I found the many of the diagrams to be a bit cryptic (such as Figure 3 and 6) and wish that these results could have been summarized in a more user-friendly manner.