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It is well known that monadic second-order logic with linear order captures exactly regular languages. On the other hand, if addition is allowed, then J.F.Lynch has proved that existential monadic secondorder logic captures at least all the languages in NTIME(n), and then expresses some NP-complete languages (e.g. knapsack problem). It seems that most combinatorial NP-complete problems (e.g...
We exhibit an NP-complete problem defined by an existential monadic second-order (EMSO) formula over functional structures that is: 1 minimal under several syntactic criteria (i.e., any EMSO formula that further strengthens any criterion defines a PTIME problem even if all other criteria are weakened); 2 unique for such restrictions, up to renamings and symmetries...
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