We define the reachability-bound problem to be the problem of finding a symbolic worst-case bound on the number of times a given control location inside a procedure is visited in terms of the inputs to that procedure. This has applications in bounding resources consumed by a program such as time, memory, network-traffic, power, as well as estimating quantitative properties (as opposed to boolean properties) of data in programs, such as information leakage or uncertainty propagation. Our approach to solving the reachability-bound problem brings together two different techniques for reasoning about loops in an effective manner. One of these techniques is an abstract-interpretation based iterative technique for computing precise disjunctive invariants (to summarize nested loops). The other technique is a non-iterative proof-rules based technique (for loop bound computation) that takes over the role of doing inductive reasoning, while deriving its power from the use of SMT solvers to reason about abstract loop-free fragments. Our solution to the reachability-bound problem allows us to compute precise symbolic complexity bounds for several loops in .Net base-class libraries for which earlier techniques fail. We also illustrate the precision of our algorithm for disjunctive invariant computation (which has a more general applicability beyond the reachability-bound problem) on a set of benchmark examples.

Providing feedback on programming assignments is a tedious task for the instructor, and even impossible in large Massive Open Online Courses with thousands of students. Previous research has suggested that program repair techniques can be used to generate feedback in programming education. In this paper, we present a novel fully automated program repair algorithm for introductory programming assignments. The key idea of the technique, which enables automation and scalability, is to use the existing correct student solutions to repair the incorrect attempts. We evaluate the approach in two experiments: (I) We evaluate the number, size and quality of the generated repairs on 4,293 incorrect student attempts from an existing MOOC. We find that our approach can repair 97% of student attempts, while 81% of those are small repairs of good quality. (II) We conduct a preliminary user study on performance and repair usefulness in an interactive teaching setting. We obtain promising initial results (the average usefulness grade 3.4 on a scale from 1 to 5), and conclude that our approach can be used in an interactive setting. CCS Concepts • Applied computing → Computerassisted instruction; • Software and its engineering → Software testing and debugging;