Update

Sorry for the delay! Our group has been busy reading a paper describing the implementation of MiniSAT (http://minisat.se/downloads/MiniSat.pdf).  We've tried to carefully dissect this paper to understand the how it solves SAT problems.  So far we have made very good progress on this task and have a decent understanding of how it works. We have also adjusted the MiniSAT code so that it outputs a file that we can run on a dot renderer to produce a primitive graph.  We spent a lot of time designing the graph and each implemented our own sort of graph.  We presented our graphs to our advisers who gave us input on them.  We just implemented a data structure that holds the node information of the graph.  Our plan is to finish polishing up the graph and then move toward the animation. 

-Mary

Week 4 Update

During week four we tried to compile MiniSAT on our own laptops and tried to get started using and IDE (VisualStudio 2010 or Eclispe).  In the past I've found that using one of these IDE's dramatically decreases the time I spend debugging and programming in general.  However, I've run into issues with libraries so I haven't quite been able to start programming using one of the IDE's, as of now I'm still using Notepad++.  Also this week we started iintroducing print statements to the MiniSAT code to visualize how it is solving the SAT and began testing it on small, simple problems.  We were able to see where MiniSAT was making "assumptions" (instantiating a variable) and propagating other variables based on these assumptions, but we couldn't find a problem where we were able to see  MiniSAT backtracking.  We tried several Unsat problems with 100 or 200 variables and several constraints with no luck.  Fortunately, Dr. Dwyer found a SAT visualizer that came with a file that backtracked so we finally have been able to see how MiniSAT backtracks :).  We still want to make our own visualizer and will this upcoming week discuss what we like and don't like in the visualize Dr. Dwyer found (DPVIS – A Tool to Visualize the Structure of SAT Instances ). 

Further, Dr. Choueiry suggested that we look at how cconflicts are identified by CBJ,  test whether those conflicts are discovered more than once during search, and test whether they are global.  Perhaps this will be the topic of one of our posters :).

-Mary

Week 2-3

These last few weeks we have continued our discussion about SAT problems.  After understanding the format of the benchmark problems and running into a few issues compiling MiniSAT, we finally got the benchmark problems to run on MiniSAT AND produce the correct results :).  We decided our next task is to dig into the MiniSAT code and try to understand how it works to solve the problems.  To do this we decided to form a graph displaying what steps the solver is taking to solve each benchmark.  We are in the process adding code to MiniSAT so that the graph is generated when the as the problem is being solved.  Eventually what we would like to do is have a sort of animation of how MiniSAT is solving a problem.  Right now, we are working to get the code compiling on our own computers (not using the CSE remote computer).

-Mary

Week One (Second Semester)

This week we started our weekly meetings again.  This semester we are planning on meeting twice weekly as a group.  Our meetings this semester will be more discussion based in comparison to last semester. This semester we are starting the SAT side of our research and including Elena and Dr. Dwyer in more in our discussions.  We have started comparing some of the techniques of both fields and are noticing that a lot of the same concepts exist in both fields.  For example a BCP (Boolean Constraint Propagation) in SAT is similar to the domino effect in CSPs.  For the first week we decided to explore SAT using a SAT solver, particularly miniSAT. As of right now, I have downloaded it and (finally) figured out how to compile it.  I plan on looking at some benchmark problems and trying to understand how it works J.

Kick-off meeting for Spring 2012

The entire team (2 ugrad students, Maggie and Mary, 2 grad mentors, Elena and Robert, and 2 faculty sponsors, Matt and Berthe) met for a relaxed meeting on January 6, 2012 at the Oven (Indian restaurant).  We discussed what was accomplished during Fall 2011 (where we focused on studying fundamental CP concepts and implementing search, backtracking, and consistency algorithms).  We agreed to start Spring 2012 by reverse engineering MiniSAT (SAT solver), studying SMT solvers, then diving into the study of constraints that arise in program analysis.  We will be meeting twice per week.  Most likely as follows: Once as a team to discuss progress and once as a smaller team to read tutorial papers.   Below is a photo of the super team taken at the Oven.  From left to right:  Elena, Matt, Berthe, Maggie, Robert,  and Mary.

End of semester meeting, Dec, 22, 2011

On December 22nd, 2011, we met at the Oven (Indian restaurant) for a relaxed brainstorming meeting.  Dr. Dwyer was in South Africa and could not join us.  Elena Sherman (graduate mentor) came to the restaurant, looked around for us, but could not find us although we were seated at the entrance (mishaps occur...), and left :-(   We are sorry, Elena, but we will coordinate better next time.  Were able to attend:  Mary, Maggie, Robert (graduate mentor), and Berthe.  During the dinner, we discussed the joys and difficulties of the fall semester and decided to delay any discussion about the Spring semester to another meeting that Matt and Elena can attend.  After the dinner, we took the photo below, which shows, from left to right, Robert, Mary, and Maggie.  Berthe took the photo.

Midyear Summary

The end of the semester was spent implementing more complex look-ahead schemas with better backtracking algorithms. This included implementing FC (Forward-Checking), FC-CBJ, and AC-2001, an improved arc-consistency algorithm.

FC is one of the best look-ahead schemas for CSPs—it is strong when dealing with CSPs of low tightness (few constraints) as well as CSPs with high tightness and high density (many constraints, many variables). When FC is paired with CBJ, it can be a very powerful search tool. This is due to the fact that FC is good at eliminating future paths in the search space, while CBJ is good at reducing the number of backtracks that occur during the search, making for a faster search all-around.

FC is a difficult algorithm to implement at first—its methods are somewhat different from your typical backtracking algorithms. In FC, you are using the current assignment of variables to eliminate future assignments that are not consistent with the partial assignment. It is also important to ensure that FC backtracks properly when domain wipe-out occurs—that is, if a certain assignment of variables causes a future assignment of a variable to be inconsistent, the algorithm must backtrack and form a new partial assignment. In my opinion, the most difficult part of implementing FC is managing domain values. It is a little tricky combining FC and CBJ, but is a lot easier if both are implemented separately first.

Another method of look-ahead is MAC (Maintaining Arc-Consistency). MAC performs a look-ahead in which a form of AC is run on the uninstantiated variables of the CSP. However, MAC is much more expensive than FC and performs better on CSPs of low density and high tightness. However, when graphically comparing the performances of FC and MAC, it is apparent that MAC uses more resources for problems with very low and very high tightness. MAC tends to make more constraint checks during look-ahead that save on backtracking, but do not make it a more efficient algorithm than FC.

We explored many other topics as well, such as search orders in CSPs. Search order can refer to variable order or value order, and the order in which variables are instantiated or values are chosen can have a great impact on the speed of an algorithm. A few ordering heuristics include min-conflict, cruciality, and promise. We implemented many ordering heuristics in our CSP solvers in order to compare the performance of our algorithms on random instances using different variable orderings.

We also examined GAC (Generalized Arc-Consistency) and studied Regín’s algorithm for applying it to a CSP with an All different constraint applying to its variables. The algorithm requires that the CSP be represented as a bipartite graph consisting of variables and the set union of all domain values. Then, a maximal matching must be found such that no two edges share a vertex. A value can be removed from the domain if its edge is not part of the matching, if it is not a strongly connected component, and if it does not begin at a free vertex.  

All in all, I felt that I learned much this semester. While my main struggle was debugging my code and finding time in my busy schedule to do so, I feel that my programming and reasoning skills have improved and that this research opportunity has been very positive. I look forward to continuing next semester!

-Maggie