Flexible Probabilistic Modeling for Search Based Test Data Generation

While Search-Based Software Testing (SBST) has improved significantly in the last decade we propose that more flexible, probabilistic models can be leveraged to improve it further. Rather than searching for an individual, or even sets of, test case(s) or datum(s) that fulfil specific needs the goal can be to learn a generative model tuned to output a useful family of values. Such generative models can naturally be decomposed into a structured generator and a probabilistic model that determines how to make non-deterministic choices during generation. While the former constrains the generation process to produce valid values the latter allows learning and tuning to specific goals. SBST techniques differ in their level of integration of the two but, regardless of how close it is, we argue that the flexibility and power of the probabilistic model will be a main determinant of success. In this short paper, we present how some existing SBST techniques can be viewed from this perspective and then propose additional techniques for flexible generative modelling the community should consider. In particular, Probabilistic Programming languages (PPLs) and Genetic Programming (GP) should be investigated since they allow for very flexible probabilistic modelling. Benefits could range from utilising the multiple program executions that SBST techniques typically require to allowing the encoding of high-level test strategies

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem -- or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (but possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORSs, and confirmed that the procedure works well through preliminary experiments that are reported at the end of the article