Inferring Lower Runtime Bounds for Integer Programs

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples

Proving Non-Termination via Loop Acceleration

We present the first approach to prove non-termination of integer programs that is based on loop acceleration. If our technique cannot show non-termination of a loop, it tries to accelerate it instead in order to find paths to other non-terminating loops automatically. The prerequisites for our novel loop acceleration technique generalize a simple yet effective non-termination criterion. Thus, we can use the same program transformations to facilitate both non-termination proving and loop acceleration. In particular, we present a novel invariant inference technique that is tailored to our approach. An extensive evaluation of our fully automated tool LoAT shows that it is competitive with the state of the art

Alternating runtime and size complexity analysis of integer programs

We present a modular approach to automatic complexity analysis. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer size bounds on program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. Extensive experiments with the implementation of our method demonstrate its performance and power in comparison with other tools

Analyzing runtime and size complexity of integer programs

We present a modular approach to automatic complexity analysis of integer programs. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer bounds on the absolute values of program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. The bounds computed by our method are polynomial or exponential expressions that depend on the absolute values of input parameters. We show how to extend our approach to arbitrary cost measures, allowing to use our technique to find upper bounds for other expended resources, such as network requests or memory consumption. Our contributions are implemented in the open source tool KoAT, and extensive experiments show the performance and power of our implementation in comparison with other tools