Realizable Paths and the NL vs L Problem

A celebrated theorem of Savitch [Sav70] states that NSPACE(S) ⊆ DSPACE(S2 ). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log2 n) space, implying NL ⊆ DSPACE(log2 n). While Savitch’s theorem itself has not been improved in the last four decades, studying the space complexity of several special cases of STCONNECTIVITY has provided new insights into the space-bounded complexity classes. In this paper, we introduce new kind of graph connectivity problems which we call graph realizability problems. All of our graph realizability problems are generalizations of UNDIRECTED STCONNECTIVITY. ST-REALIZABILITY, the most general graph realizability problem, is LogCFLcomplete. We define the corresponding complexity classes that lie between L and LogCFL and study their relationships. As special cases of our graph realizability problems we define two natural problems, BALANCED ST-CONNECTIVITY and POSITIVE BALANCED ST-CONNECTI...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Shiva Kintali
• Keywords: CORR 2010, Education, Graph Realizability Problems, Special Cases, ST-CONNECTIVITY