Detlef Dr. Fehrer

Presenting inequations in mathematical proofs

Logical systems, such as deductive planning approaches and formal methods in software verification, increasingly make use of machine generated proofs, and the size of these is growing continuously. Their presentation, however, is often inadequate in large portions, because the internal proof structures differ significantly from presentation styles adequate for humans. Addressing improvements in a specific and frequently occurring aspect of proof presentation, this paper describes an approach to building chains of inequations and presenting them in a compact notation format. The methods used comprise restructuring techniques, the omission of redundant information motivated by the addressees inferential capabilities, and the skillful use of a compact notation format. Our approach constitutes an important contribution to presenting mathematical proofs in a natural and human-oriented way.

Accurate ICP-based floating-point reasoning

In scientific and technical software, floating-point arithmetic is often used to approximate arithmetic on physical quantities natively modeled as reals. Checking properties for such programs (e.g. proving unreachability of code fragments) requires accurate reasoning over floating-point arithmetic. Currently, most of the SMT-solvers addressing this problem class rely on bit-blasting. Recently, methods based on reasoning in interval lattices have been lifted from the reals were they traditionally have been successful) to the floating-point numbers. The approach presented in this paper follows the latter line of interval-based reasoning, but extends it by including bitwise integer operations and cast operations between integer and floating-point arithmetic. Such operations have hitherto been omitted, as they tend to define sets not concisely representable in interval lattices, and were consequently considered the domain of bit-blasting approaches. By adding them to interval-based reasoning, the full range of basic data types and operations of C programs is supported. Furthermore, we propose techniques in order to mitigate the problem of aliasing during interval reasoning. The experimental results confirm the efficacy of the proposed techniques. Our approach outperforms solvers relying on bit-blasting