The notion of Las Vegas algorithm was introduced by Babai (1979) and may be defined in two ways: * In Babai's original definition, a randomized algorithm is called Las Vegas if it has finitely bounded running time and certifiable random failure. * Alternatively, in a widely accepted definition today, Las Vegas algorithms mean the zero-error randomized algorithms with random running time. The equivalence between the two definitions is straightforward. In particular, by repeatedly running the algorithm until no failure encountered, one can simulate the correct output of a successful running. We show that this can also be achieved for distributed local computation. Specifically, we show that in the LOCAL model, any Las Vegas algorithm that terminates in finite time with locally certifiable failures, can be converted to a zero-error Las Vegas algorithm, at a polylogarithmic cost in the time complexity, such that the resulting algorithm perfectly simulates the output of the original algorithm on the same instance conditioned on that the algorithm successfully returns without failure.

翻译：拉斯维加斯算法的概念由Babai（1979）提出，可通过两种方式定义：* 在Babai的原始定义中，若随机化算法具有有限有界运行时间且可验证的随机失败，则称为拉斯维加斯算法。* 而在当今广泛接受的定义中，拉斯维加斯算法指具有随机运行时间的零错误随机化算法。两种定义之间的等价性显而易见。特别地，通过反复运行算法直至不遇到失败，可模拟成功运行的正确输出。我们证明这一结论对分布式局部计算同样成立。具体而言，我们证明在LOCAL模型中，任何具有有限终止时间且具备局部可验证失败机制的拉斯维加斯算法，均可在时间复杂度的多对数代价内转化为零错误拉斯维加斯算法，使得所得算法在原始算法成功返回无失败输出的条件下，完美模拟同一实例上原始算法的输出。