# Complete problems for logspace involving lexicographic first paths in graphs

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## Abstract

It is shown that the problem of deciding whether a given vertex is on the lexicographic first path of some digraph, starting at some other specified vertex, is complete for deterministic logspace via projection translations: such translations are extremely weak forms of reductions. Other related problems involving constrained versions of the lexicographically first path problem in both digraphs and graphs are also shown to be similarly complete. The methods used to prove completeness involve the consideration of decision problems as sets of finite structures satisfying certain logical formulae.

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