Undirected ST-Connectivity in Log-Space

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log 4/3 (·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic log-space computations). Our algorithm also implies log-space constructible universal-traversal sequences for graphs with restricted labelling and log-space constructible universal-exploration sequences for general graphs