Marc Brockschmidt

Automated Termination Analysis of Java Bytecode by Term Rewriting.

We present an automated approach to prove termination of Java Bytecode (JBC) programs by automatically transforming them to term rewrite systems (TRSs). In this way, the numerous techniques and tools developed for TRS termination can now be used for imperative object-oriented languages like Java, which can be compiled into JBC.

Better termination proving through cooperation

One of the difficulties of proving program termination is managing the subtle interplay between the finding of a termination argument and the finding of the arguments supporting invariant. In this paper we propose a new mechanism that facilitates better cooperation between these two types of reasoning. In an experimental evaluation we find that our new method leads to dramatic performance improvements.

Proving Termination of Programs Automatically with AProVE

AProVE is a system for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and term rewrite systems (TRSs). To analyze programs in high-level languages, AProVE automatically converts them to TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting TRSs. The generated proofs can be exported to check their correctness using automatic certifiers. For use in software construction, we present an AProVE plug-in for the popular Eclipse software development environment.

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.

Automated termination proofs for Java programs with cyclic data

In earlier work, we developed a technique to prove termination of Java programs automatically: first, Java programs are automatically transformed to term rewrite systems (TRSs) and then, existing methods and tools are used to prove termination of the resulting TRSs. In this paper, we extend our technique in order to prove termination of algorithms on cyclic data such as cyclic lists or graphs automatically. We implemented our technique in the tool AProVE and performed extensive experiments to evaluate its practical applicability.

Modular Termination Proofs of Recursive Java Bytecode Programs by Term Rewriting

In [5, 15] we presented an approach to prove termination of non-recursive Java Bytecode (JBC) programs automatically. Here, JBC programs are first transformed to finite termination graphs which represent all possible runs of the program. Afterwards, the termination graphs are translated to term rewrite systems (TRSs) such that termination of the resulting TRSs implies termination of the original JBC programs. So in this way, existing techniques and tools from term rewriting can be used to prove termination of JBC automatically. In this paper, we improve this approach substantially in two ways: (1) We extend it in order to also analyze recursive JBC programs. To this end, one has to represent call stacks of arbitrary size. (2) To handle JBC programs with several methods, we modularize our approach in order to reuse termination graphs and TRSs for the separate methods and to prove termination of the resulting TRS in a modular way. We implemented our approach in the tool AProVE. Our experiments show that the new contributions increase the power of termination analysis for JBC significantly. 1998 ACM Subject Classification D.1.5 - Object-oriented Programming, D.2.4 - Software/Program Verification, D.3.3 - Language Constructs and Features, F.3 - Logics and Meanings of Programs, F.4.2 - Grammars and Other Rewriting Systems, I.2.2 - Automatic Programming

Analyzing Program Termination and Complexity Automatically with AProVE

In this system description, we present the tool AProVE for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and rewrite systems. In addition to classical term rewrite systems (TRSs), AProVE also supports rewrite systems containing built-in integers (int-TRSs). To analyze programs in high-level languages, AProVE automatically converts them to (int-)TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting rewrite systems. The generated proofs can be exported to check their correctness using automatic certifiers. To use AProVE in software construction, we present a corresponding plug-in for the popular Eclipse software development environment.

T2: Temporal Property Verification

We present the open-source tool T2, the first public release from the TERMINATOR projecti??[9]. T2 has been extended over the past decade to support automatic temporal-logic proving techniques and to handle a general class of user-provided liveness and safety properties. Input can be provided in a native format and in C, via the support of the LLVM compiler framework. We briefly discuss T2s architecture, its underlying techniques, and conclude with an experimental illustration of its competitiveness and directions for future extensions.

The COST IC0701 verification competition 2011

This paper reports on the experiences with the program verification competition held during the FoVeOOS conference in October 2011. There were 6 teams participating in this competition. We discuss the three different challenges that were posed and the solutions developed by the teams. We conclude with a discussion about the value of such competitions and lessons learned from them.

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 the use of 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.