With the growing number of commercial cloud-computing services, there is a corresponding need to verify that such computations were performed correctly. In other words, after a weak client outsources computations to an untrusted cloud, it must be able to ensure the correctness of the results with less work than re-performing the computations. This is referred to as verifiable computation. In this paper we present a new probabilistic verifiable computation method based on a novel Reversible Physically Unclonable Function (PUF) and a binomial Bayesian Inference model. Our scheme links the outsourced software with the cloud-node hardware to provide a proof of the computational integrity and the resultant correctness of the results with high probability. The proposed Reversible SW-PUF is a two-way function capable of computing partial inputs given its outputs. Given the random output signature of a specific instruction in a specific basic block of the program, only the computing platform that originally computed the instruction can accurately regenerate the inputs of the instruction correct within a certain number of bits. To explore the feasibility of the proposed design, the Reversible SW-PUF was implemented in HSPICE using 45 nm technology. The probabilistic verifiable computation scheme was implemented in C++, and the Bayesian Inference model was utilized to estimate the probability of correctness of the results returned from the cloud service. Our proof-of-concept implementation of Reversible SW-PUF exhibits good uniqueness compared to other types of PUFs and exhibits perfect reliability and acceptable randomness. Finally, we demonstrate our verifiable computation approach on a matrix computation. We show that it enables faster verification than existing verification techniques.