Evaluation of the ProB Constraint Solver Sample Clauses

Evaluation of the ProB Constraint Solver. Various industrial applications have shown the need for improved constraint-solving capabilities (see CBC Deadlock, Test-Case Generation). In order to evaluate ProB, and detect areas for improvement, we have studied to what extent classical constraint satisfaction problems can be conveniently expressed as B predicates, and then solved by ProB. In particular, we have studied problems such as the n-Queens problem, graph colouring, graph isomorphism detection, time tabling, Sudoku, Hanoi, magic squares, Alphametic puzzles, and several more. We have then compared the performance with respect to other tools, such as the model checker TLC for TLA+, AnimB for Event-B, and Alloy. The experiments show that some constraint satisfaction problems can be expressed very conveniently in B and solved very effectively with ProB. For example, TLC takes 8747 seconds (2 hours 25 minuts) to solve the 9-queens problem expressed as a logical predicate; Alloy 4.1.10 with minisat takes 0.406 seconds, ProB 1.3.3 takes 0.01 seconds. For 32 queens, ProB 1.3.3 takes 0.28 seconds, while Xxxxx 4.1.10 with minisat takes over 4 minutes (TLC was only able to solve the n-queens problem up until n=9, or n=14 when reformulating the problem as a model checking problem rather than a constraint-solving problem). In another small experiment, we checked whether two graphs with 9 nodes of out-degree exactly one are isomorphic by checking for the existence of a permutation which preserved the graph structure. TLC finds a permutation after 2 hours 6 minutes and 28 seconds; ProB 1.3.3 takes 0.01 seconds to find the same solution, while Xxxxx takes 0.11 seconds with SAT4J and 0.05 seconds with minisat. For some other examples (in particular time-tabling) involving operators such as the relational image, the performance of ProB is still sub-optimal with respect to, e.g., Alloy; we plan to overcome this shortcoming in the future. Our long term goal is that B can not only be used to as a formal method for developing safety critical software, but also as a high-level constraint programming language.
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