Characterizing Arithmetic Read-Once Formulae

An \emph{arithmetic read-once formula} (ROF for short) is a formula (i.e. a tree of computation) in which the operations are $\{+,\times\}$ and such that every input variable labels at most one leaf. We give a simple characterization of such formulae. Other than being interesting in its own right, our characterization gives rise to a property testing algorithm for functions computable by such formulae. To the best of our knowledge, prior to our work no characterization and/or property testing algorithm was known for this kind of formulae

Model Learning: A Survey on Foundation, Tools and Applications

The quality and correct functioning of software components embedded in electronic systems are of utmost concern especially for safety and mission-critical systems. Model-based testing and formal verification techniques can be employed to enhance the reliability of software systems. Formal models form the basis and are prerequisite for the application of these techniques. An emerging and promising model learning technique can complement testing and verification techniques by providing learned models of black box systems fully automatically. This paper surveys one such state of the art technique called model learning which recently has attracted much attention of researchers especially from the domains of testing and verification. This survey paper reviews and provides comparison summaries highlighting the merits and shortcomings of learning techniques, algorithms, and tools which form the basis of model learning. This paper also surveys the successful applications of model learning technique in multidisciplinary fields making it promising for testing and verification of realistic systems.Comment: 43 page