Koepke Machines and Satisfiability for Infinitary Propositional Languages

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10307)


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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Merlin Carl
    • 1
    • 2
  • Benedikt Löwe
    • 3
    • 4
    • 5
  • Benjamin G. Rin
    • 6
  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Fakultät für Informatik und MathematikUniversität PassauPassauGermany
  3. 3.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  4. 4.Fachbereich MathematikUniversität HamburgHamburgGermany
  5. 5.Christ’s College, Churchill College, and Faculty of MathematicsUniversity of CambridgeCambridgeEngland
  6. 6.Departement Filosofie En ReligiewetenschapUniversiteit UtrechtUtrechtThe Netherlands

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