In this paper, we define the language (FO + posHP), where HP is the Hamiltonian path operator, and show that a problem can be represented by a sentence of this language if and only if the problem is in NP. We also show that every sentence of this language can be written in a normal form, and so establish the fact that the problem of deciding whether there is a directed Hamiltonian path between two distinguished vertices of a digraph is complete for NP via projection translations: as far as we know, this is the first such problem discovered. We also give a general technique for extending existing languages using operators derived from problems.
CITATION STYLE
Stewart, I. A. (1990). Using the hamiltonian path operator to capture NP. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 468 LNCS, pp. 134–143). Springer Verlag. https://doi.org/10.1007/3-540-53504-7_70
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