Abstract
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.
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© 1991 Springer-Verlag Berlin Heidelberg
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Stewart, I.A. (1991). Using the hamiltonian path operator to capture NP. In: Akl, S.G., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '90. ICCI 1990. Lecture Notes in Computer Science, vol 468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53504-7_70
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DOI: https://doi.org/10.1007/3-540-53504-7_70
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