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Mechanising Complexity Theory: The Cook-Levin Theorem in Coq

Lennard Gäher, Fabian Kunze, Liron Cohen, Cezary Kaliszyk
We mechanise the Cook-Levin theorem, i.e. the NP-completeness of SAT, in the proof assistant Coq.  ...  To the best of our knowledge, this is the first result in computational complexity theory that has been mechanised with respect to any concrete computational model.  ...  We conjecture that many interesting results in computational complexity theory can be mechanised when phrased in terms of L, as evident by a mechanisation of the time hierarchy theorem we are working on  ... 
doi:10.4230/lipics.itp.2021.20 fatcat:s7pfruurijg2jeeopie27jd7ge

Computability in constructive type theory [article]

Yannick Forster, Universität Des Saarlandes
We give a formalised and machine-checked account of computability theory in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant.  ...  of the Coq Library of Undecidability Proofs.  ...  Mechanising Complexity Theory: The Cook-Levin Theorem in Coq. [ 189 ] 189 Post. 1944 .  ... 
doi:10.22028/d291-35758 fatcat:deb5muacebhsnnmk5p25mgc7ia