Wednesday, July 16, 2008

Highland workshop on XML, Logic, and Automata

I'll be attending Highlands Workshop on XML, Logic, and Automata organized by Leonid from tomorrow until this Sunday. The venue is actually quite interesting: a small town in the Highlands called Grantown-on-spey. I'm just hoping that they have a grocery store :) I will give a presentation on recurrent reachability in regular model checking based on this paper. Anyway, I'll post a summary of the workshop later on this week.

Monday, July 14, 2008

Rahul Santhanam has joined Edinburgh

Rahul Santhanam, Lance Fortnow's ex PhD student, has recently joined Edinburgh's School of Informatics. Warm welcome to him!

Wednesday, July 02, 2008

Finite-variable hierarchy conjecture

It seems that Ben Rossman has resolved another long-standing open problem in finite model theory: finite-variable hierarchy conjecture. Loosely speaking, the conjecture is that over ordered graphs first-order logic with k+1 variable is more powerful than first-order logic with k variable. The problem is nicely summarized in Anuj Dawar's survey. Ben has shown that this hierarchy is strict. What was previously known is that (over ordered graphs) first-order logic with 3 variables is strictly more expressive than first-order logic with 2 variables, but it was not known whether first-order logic with 3 variables is less expressive than first-order logic with k variables, for every k > 3. Worse yet, it wasn't even known whether this hierarchy is strict. See Anuj Dawar's survey for further details.

I believe this is the third big open problems that Ben has resolved in this decade. Go Ben!