## Section: New Results

### Static single information form: debunking

Participants : Benoit Boissinot, Philip Brisk [ EPFL, Lausanne ] , Alain Darte, Fabrice Rastello.

The static single information (SSI) form, proposed by Ananian, then in a more general form by Singer, is an extension of the static single assignment (SSA) form. The fact that interference graphs for procedures represented in SSA form is chordal is a nice property that initiated our work on register allocation under SSA form. Several interesting results have also been shown for SSI concerning liveness analysis and representation of live-ranges of variables, which could make SSI appealing for just-in-time compilation. In particular, the chordal property for SSA has motivated Brisk and Sarrafzadeh is 2007 to prove a similar result concerning SSI: the interference graph is an interval graph. Unfortunately, previous literature on SSI is sparse, appears to be partly incorrect, including the proof on interval graphs, and based on several inaccurate claims and theories (in particular the program structure tree of Johnson et al.). Our paper corrects some of the mistakes that have been made. Our main result is a complete proof that, even for the most general definition of SSI, it is possible to define a total order on basic blocks, and thus on program points, so that live-ranges of variables correspond to intervals. Our proof is based on the notion of loop nesting forest.

This work is the result of an informal collaboration with Philip Brisk from the University of Lausanne (EPFL).