Abstract
Fischer and Rabin proved in [4] that Presburger Arithmetic has at least double exponential worse-case complexity. In [6] a theory of generic-case complexity was developed, where algorithmic problems are studied on most inputs instead of all set of inputs. An interesting question rises about existing of more efficient (say, polynomial) generic algorithm deciding Presburger Arithmetic on some set of closed formulas. We prove, however, that there is no even exponential generic algorithm working correctly on arbitrary very large sets of inputs (so-called strongly generic sets).
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