Abstract
We consider complexity theory for Koepke machines, also known as Ordinal Turing Machines (OTMs), and define infinitary complexity classes \(\infty \)-\(\mathbf {P}\) and \(\infty {\text {-}}\mathbf {NP}\) and the OTM analogue of the satisfiability problem, denoted by \(\infty {\text {-}}\mathrm {SAT}\). We show that \(\infty {\text {-}}\mathrm {SAT}\) is in \(\infty {\text {-}}\mathbf {NP}\) and \(\infty {\text {-}}\mathbf {NP}\)-hard (i.e., the problem is \(\infty {\text {-}}\mathbf {NP}\)-complete), but not OTM decidable.
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Carl, M., Löwe, B., Rin, B.G. (2017). Koepke Machines and Satisfiability for Infinitary Propositional Languages. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_19
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DOI: https://doi.org/10.1007/978-3-319-58741-7_19
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