Better Veri cation Through Symmetry

A fundamental diiculty in automatic formal veriication of nite-state systems is the state explosion problem { even relatively simple systems can produce very large state spaces, causing great dii-culties for methods that rely on explicit state enumeration. We address the problem by exploiting structural symmetries in the description of the system to be veriied. We make symmetries easy to detect by introducing a new data type scalarset, a nite and unordered set, to our description language. The operations on scalarsets are restricted so that states are guaranteed to have the same future behaviors, up to permutation of the elements of the scalarsets. Using the symmetries implied by scalarsets, a veriier can automatically generate a reduced state space, on the y. We provide a proof of the soundness of the new symmetry-based veriication algorithm based on a deenition of the formal semantics of a simple description language with scalarsets. The algorithm has been implemented and evaluated on several realistic high-level designs. Memory requirements were reduced by amounts ranging from 83% to over 99%, with speedups ranging from 65% to 98%. Symmetry-based reduction leads to an alternative characterization of data independence: a protocol is data-independent if there is a scalarset type not used as an array index or for loop index. In this case, symmetry-based reduction converts an innnite state space to a nite state space. Unlike other methods that exploit data independence in veriication, this reduction occurs completely automatically.