Abstract is a tool to automatically infer complexity bounds and prove termination of (possibly recursive) integer programs. To this end, implements an alternating modular inference of upper runtime and size bounds for program parts. In particular, uses a portfolio of different techniques to analyze subprograms. The power of our approach is demonstrated by an extensive experimental evaluation.

Abstract There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops) , where questions regarding the runtime and the size of variable values are decidable and where we can therefore obtain techniques that are “complete” for such subclasses. We show how to use these results for the complexity analysis of arbitrary general integer programs. To this end, we present a modular approach which computes local runtime and size bounds for subprograms which correspond to prs -loops. These local bounds are then lifted to global runtime and size bounds for the whole integer program. Furthermore, we introduce several techniques to transform larger programs into prs -loops to increase the scope of the approach. The power of the procedure is shown by our implementation in the complexity analysis tool .

We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all programs that consist of a single loop, with a linear loop guard and a loop body composed of two linear commuting and diagonalizable updates. In each iteration of the loop, the update to be carried out is picked at random, according to a fixed probability. We show the decidability of UPAST for this class of programs, where the program’s variables and inputs may range over various sub-semirings of the real numbers. In this way, we extend a line of research initiated by Tiwari in 2004 into the realm of randomized programs.

Abstract Recently, we showed how to use control-flow refinement (CFR) to improve automatic complexity analysis of integer programs. While up to now CFR was limited to classical programs, in this paper we extend CFR to probabilistic programs and show its soundness for complexity analysis. To demonstrate its benefits, we implemented our new CFR technique in our complexity analysis tool .

Abstract We present a novel modular approach to infer upper bounds on the expected runtimes of probabilistic integer programs automatically. To this end, it computes bounds on the runtimes of program parts and on the sizes of their variables in an alternating way. To evaluate its power, we implemented our approach in a new version of our open-source tool .