ReachFewL = ReachUL

Authors:
Brady Garvin;Derrick Stolee;Raghunath Tewari;N. V. Vinodchandran
Affiliations:
Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, USA 68588;Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, USA 68588;Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, Kharagpur, India 721302;Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, USA 68588
Venue:
Computational Complexity
Year:
2014

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Abstract

We show that two complexity classes introduced about two decades ago are unconditionally equal. ReachUL is the class of problems decided by nondeterministic log-space machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural generalization of ReachUL, is the class of problems decided by nondeterministic log-space machines which on every input have at most polynomially many computation paths from the start configuration to any other configuration. We show that ReachFewL = ReachUL.