Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint Transition Systems, a program abstraction where termination is decidable. We show that these programs also have a decidable complexity property: one can determine whether the length of all transition sequences can be bounded in terms of the initial state. This is the bounded termination problem. Interestingly, if a bound exists, it must be polynomial. We prove that the bounded termination problem is PSPACE-complete and, moreover, if a bound exists then a symbolic bound which is constant-factor tight (as a univariate polynomial) can be computed in PSPACE. We present this computation in the form of computing a reachability bound, a bound on the number of visits to a given program location. This presentation is inspired by the practical usefulness of this problem formulation. We also discuss, theoretically, the use of bounds on the abstract program to infer conclusions on a concrete program that has been abstracted. The conclusion maybe a polynomial time bound, or in other cases polynomial space or exponential time. We argue that the monotonicity-constraint abstraction promises to be useful for practical complexity analysis of programs.

Current tools for automated deduction are often powerful and complex. Due to their complexity there is a risk that they contain bugs and thus deliver wrong results. To ensure reliability of these tools, one possibility is to develop certifiers which check the results of tools with the help of a trusted proof assistant. We present a framework which illustrates the essential steps to develop stand-alone certifiers which efficiently check generated proofs outside the employed proof assistant. Our framework has already been used to develop certifiers for various properties, including termination, confluence, completion, and tree automata related properties.

Abstract—Classical approaches for program analysis as, e.g., termination analysis usually do not take into account modern software approaches such as service-oriented systems or cloud computing. Instead, they have a monolithic view on the software system as a single completely available program. As first step to enable such analyses also in a service-oriented or cloud computing context, respectively, this paper considers termination. Since termination is a service quality attribute, we consider a service-level agreement approach that allows dynamic bindings to software services. In contrast to many other service-level agreements, termination is a binary attribute that cannot be measured quantitatively (as, e.g., reliability or response time). The proposed approach shows how clients of services can verify the information provided by the services.