I am far from being an expert on descriptive complexity, and have only skimmed the paper. One spot jumped out at me as a potential error: on page 21, the senten

I am far from being an expert on descriptive complexity, and have only skimmed the paper. One spot jumped out at me as a potential error: on page 21, the sentence "Next we exploit that a choice in state S will be insignificant iff all update sets in Delta_r(S) are isomorphic, so..." seems suspicious to me. One direction is likely obvious (that an isomorphism between choices proves the insignificance of the choice), but the other direction seems likely to be untrue (if I am interpreting correctly).