Talk:St-connectivity

Instead of "Map all possible states of the deterministic log-space machine to vertices of a graph, and put an edge between u and v if the state v can be reached from u within one step of the non-deterministic machine.", shouldn't it be: "Map all possible states of M to vertices of a graph, and put an edge between u and v if the state v can be reached from u within one step of the machine M."? — Preceding unsigned comment added by Marek bielik (talk • contribs) 17:54, 14 January 2018 (UTC)

"In particular, the problem of st-connectivity is actually NL-complete, that is, every problem in the class NL is reducible to connectivity under a log-space reduction. This remains true for the stronger case of first-order reductions (Immerman 1999, p. 51)."

This contradicts the article on First-order reduction which says that log-space reductions are stronger than first-order reductions. I've seen this a lot, I am not sure what the proper definitions of "weak" and "strong" reductions should be, but many articles are confused on this. --74.194.27.5 (talk) 13:44, 16 December 2007 (UTC)

No, they are both correct. First-order reduction is weaker than log-space, so saying something holds under first-order reductions is a stronger statement than saying the same thing holds under log space reductions. Suppose that A is a weaker assumption than B. This means that proving A -> C is a stronger statement than proving B -> C. The idea is that it's 'easy' to prove something with a powerful tool, so the statement is weaker. —Preceding unsigned comment added by 66.90.167.14 (talk) 07:25, 10 April 2008 (UTC)

"Connectivity is solvable in deterministic logspace, as per <a href=http://portal.acm.org/citation.cfm?id=1060647>this</a> paper." is misleading since the paper refers to the undirected problem. It is unknown if connectivity in DIRECTED GRAPHS can be solved in deterministic log space. If it could be, Savitch's theorem could be improved. The way the current article is written implies that this is the case and we can improve Savitch's theorem. —Preceding unsigned comment added by 128.100.5.116 (talk) 15:17, 22 October 2008 (UTC)

What is an alternating graph? —Preceding unsigned comment added by 134.58.45.38 (talk) 12:48, 24 March 2009 (UTC)

Yeah, google doesn't know what an alternating graph is. — Preceding unsigned comment added by 83.40.90.157 (talk) 08:24, 6 June 2011 (UTC)

Although it is relatively trivial, it would be useful if this page discussed algorithms and time complexity for s-t connectivity, not just space complexity. 96.251.20.229 (talk) 23:48, 2 July 2013 (UTC)

The page needs to decide if its st connectivity or s-t connectivity (i.e., how the hyphens are used). — User:michaeln