Abstract
We define a monadic logic MonadicNLIN which is a fragment of Grandjean’s logic for the class NLIN of problems solvable in linear time on nondeterministic random-access machines. This logic operates on functional rather than the usual relational structures of finite model theory,and we adapt the notions of quantifier-free interpretation and reduction to this functional setting. We also introduce the notion of compatible successor function,which,in our setting,replaces the built- in linear order relations used in logical characterisations of complexity classes. We show that MonadicNLIN is closed under quantifier-free functional reductions,that CNF-SAT is complete for MonadicNLIN under these reductions,and that MonadicNLIN contains a large number of NP-complete problems,but not the set of connected graphs.
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Lautemann, C., Weinzinger, B. (1999). MonadicNLIN and Quantifier-Free Reductions. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_23
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DOI: https://doi.org/10.1007/3-540-48168-0_23
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