The problem of loop bound analysis can conceptually be seen as an instance of invariant generation. However, the methods used in loop bound analysis differ considerably from previous invariant generation techniques. Interestingly, there is almost no previous work comparing the two sets of techniques. In this paper, we show that loop bound analysis methods can efficiently produce invariants which are hard to prove for state-of-the-art invariant generation techniques (e.g., polynomial invariants or invariants relating many variables) and thus enrich the tool-set of invariant analysis.

. We believe that difference constraints are also a good choice for complexity and resource bound analysis because the complexity of imperative programs typically arises from counter increments and resets, which can be modeled naturally by difference constraints. In this article we propose a bound analysis based on difference constraints. We make the following contributions: (1) our analysis handles bound analysis problems of high practical relevance which current approaches cannot handle: we extend the range of bound analysis to a class of challenging but natural loop iteration patterns which typically appear in parsing and string-matching routines. (2) We advocate the idea of using bound analysis to infer invariants: our soundness proven algorithm obtains invariants through bound analysis, the inferred invariants are in turn used for obtaining bounds. Our bound analysis therefore does not rely on external techniques for invariant generation. (3) We demonstrate that difference constraints are a suitable abstract program model for automatic complexity and resource bound analysis: we provide efficient abstraction techniques for obtaining difference constraint programs from imperative code. (4) We report on a thorough experimental comparison of state-of-the-art bound analysis tools: we set up a tool comparison on (a) a large benchmark of real-world C code, (b) a benchmark built of examples taken from the bound analysis literature and (c) a benchmark of challenging iteration patterns which we found in real source code. (5) Our analysis is more scalable than existing approaches: we discuss how we achieve scalability.

Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' ≤ y + c, and describe that the value of x in the current state is at most the value of y in the previous state plus some constant c ∈ ℤ. In this paper, we argue that the complexity of imperative programs typically arises from counter increments and resets, which can be modeled naturally by difference constraints.We present the first practical algorithm for the analysis of difference constraint programs and describe how C programs can be abstracted to difference constraint programs. Our approach contributes to the field of automated complexity and (resource) bound analysis by enabling automated amortized complexity analysis for a new class of programs and providing a conceptually simple program model that relates invariant- and bound analysis.We demonstrate the effectiveness of our approach through a thorough experimental comparison on real world C code: our tool Loopus computes the complexity for considerably more functions in less time than related tools from the literature.