From High School to Higher Education

The vision of introducing computing as a literacy taught from primary school to higher and lifelong education is producing a worldwide new curriculum design and adoption. A strong research effort has involved researchers and educators to find the best ways to prepare teachers and their students for computing with an emphasis on core computer science concepts. This paper, starting from a previously developed curriculum, aims to present and discuss learning trajectories for a first course on computing aiming to presenting key concepts first, such as functions and their use. This learning trajectory is compared with a second learning trajectory presenting loop and loop invariant first and a third one presenting variable first.

CoVEGI: Cooperative Verification via Externally Generated Invariants

Software verification has recently made enormous progress due to the development of novel verification methods and the speed-up of supporting technologies like SMT solving. To keep software verification tools up to date with these advances, tool developers keep on integrating newly designed methods into their tools, almost exclusively by re-implementing the method within their own framework. While this allows for a conceptual re-use of methods, it nevertheless requires novel implementations for every new technique.In this paper, we employ cooperative verification in order to avoid re-implementation and enable usage of novel tools as black-box components in verification. Specifically, cooperation is employed for the core ingredient of software verification which is invariant generation. Finding an adequate loop invariant is key to the success of a verification run. Our framework named CoVEGI allows a master verification tool to delegate the task of invariant generation to one or several specialized helper invariant generators. Their results are then utilized within the verification run of the master verifier, allowing in particular for crosschecking the validity of the invariant. We experimentally evaluate our framework on an instance with two masters and three different invariant generators using a number of benchmarks from SV-COMP 2020. The experiments show that the use of CoVEGI can increase the number of correctly verified tasks without increasing the used resources.

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis

We present an automated procedure for synthesizing sound inductive invariants for floating-point numerical loops. Our procedure generates invariants of the form of a convex polynomial inequality that tightly bounds the values of loop variables. Such invariants are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs. Unlike previous approaches that rely on policy iteration, linear algebra or semi-definite programming, we propose a heuristic procedure based on simulation and counterexample-guided refinement. We observe that this combination is remarkably effective and general and can handle both linear and nonlinear loop bodies, nondeterministic values as well as conditional statements. Our evaluation shows that our approach can efficiently synthesize loop invariants for existing benchmarks from literature, but that it is also able to find invariants for nonlinear loops that today’s tools cannot handle.

Decidability of affine solution problems

We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over $\mathbb{Q}$, we translate a quantifier-free formula equation into an equivalent statement about affine spaces over $\mathbb{Q}$, which can then be decided by an iteration procedure.