We present novel algorithms for parallel testing of code that takes structurally complex test inputs. The algorithms build on the Korat algorithm for constraint-based generation of structurally complex test inputs. Given an imperative predicate that specifies the desired structural constraints and a finitization that bounds the desired input size, Korat performs a systematic search to generate all test inputs (within the bounds) that satisfy the constraints. We present how to generate test inputs with a parallel search in Korat and how to execute test inputs in parallel, both off-line (when the inputs are saved on disk) and on-line (when execution immediately follows generation). The inputs that Korat generates enable bounded-exhaustive testing that checks the code under test exhaustively for all inputs within the given bounds. We also describe a novel methodology for reducing the number of equivalent inputs that Korat can generate. Our development of parallel Korat and the methodolog...