Abstract
We exhibit an NP-complete problem defined by an existential monadic second-order (EMSO) formula over functional structures that is:
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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);
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unique for such restrictions, up to renamings and symmetries.
Our reductions and proofs are surprisingly very elementary and simple in comparison with some recent similar results classifying existential second-order formulas over relational structures according to their ability either to express NP-complete problems or to express only PTIME ones.
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Barbanchon, R., Grandjean, E. (2004). The Minimal Logically-Defined NP-Complete Problem. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_30
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DOI: https://doi.org/10.1007/978-3-540-24749-4_30
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