Program derivation with verified transformations — a case study

A program development methodology based on verified program transformations is described and illustrated through derivations of a high level bisimulation algorithm and an improved minimum-state DFA algorithm. Certain doubts that were raised about the correctness of an initial paper-and-pencil derivation of the DFA minimization algorithm were laid to rest by machine-checked formal proofs of the most difficult derivational steps. Although the protracted labor involved in designing and checking these proofs was almost overwhelming, the expense was somewhat offset by a successful reuse of major portions of these proofs. In particular, the DFA minimization algorithm is obtained by specializing and then extending the last step in the derivation of the high level bisimulation algorithm. Our experience suggests that a major focus of future research should be aimed towards improving the technology of machine checkable proofs — their construction, presentation, and reuse. This paper demonstrates the importance of such a technology to the verification of programs and program transformations. We believe that the utility of transformational systems to program development will ultimately rest on a practical program correctness technology. © 1996 John Wiley & Sons, Inc.     

The mathematical tourist

The Mathematical Intelligencer -     

Some general aspects of hydrogen chemisorption on metal surfaces

Chemisorption of hydrogen on metal surfaces requires the dissociation of the H₂ molecule in the first place; this process has been experimentally investigated and theoretically described in terms of multi-dimensional potential energy diagrams. The adsorption of atomic hydrogen is frequently accompanied by displacements of the metal surface atoms leading to phenomena such as layer relaxation or surface reconstruction. Especially surface reconstruction may be regarded as a precursor stage for a progressive chemical attack of the hydrogen atoms also on the bulk metal, leading to the occupation of so-called “subsurface” sites, to bulk diffusion and, finally, to hydride compound formation. All these processes depend sensitively on the crystallographic structure of the surface, and some examples for H on Rh, Co and Pd surfaces will demonstrate the general correlation between the hydrogen surface concentration and the metal's cohesive energy, surface crystallography, and its tendency to reconstruct.