Linear Time Algorithms and NP-Complete Problems

We define and study a machine model (random access machine with powerful input/output instructions) and show that for this model the classes, DLINEAR and NLINEAR, of problems computable in deterministic (resp. nondeterministic) linear time are robust and powerful. In particular DLINEAR includes most of the concrete problems commonly regarded as computable in linear time (such as graph problems: topological sorting, strong connectivity...) and most combinatorial NP-complete problems belong to NLINEAR. The interest of NLINEAR class is enhanced by the following fact: some natural NP-complete problems, for example “reduction of incompletely specified automata” (in short: RISA), are NLINEAR-complete (consequently, NLINEAR ≠ DLINEAR iff RISA ∉ DLINEAR). That notion probably strengthens NP-completeness since we argue that propositional satisfiability is not NLINEAR-complete.

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