Peter Capell

A computer‐based multi‐media tutor for beginning piano students

Abstract The Piano Tutor provides computer‐based instruction to beginning piano students. Intended as a supplement to traditional instruction, the Piano Tutor helps students by correcting mistakes before they become ingrained through practice and by teaching new material as soon as the student is ready. The Piano Tutor combines an expert system with state‐of‐the‐art music recognition software and multimedia output devices to provide a stimulating learning environment that tailors instruction to the students needs.

Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

DOI: 10.2514/1.I010178 Complex software systems are becoming increasingly prevalent in aerospace applications: in particular, to accomplish critical tasks. Ensuring the safety of these systems is crucial, as they can have subtly different behaviors under slight variations in operating conditions.This paper advocates the use of formal verification techniques and in particulartheoremprovingfor hybridsoftware-intensivesystemsasawell-foundedcomplementaryapproachtothe classical aerospace verification and validation techniques, such as testing or simulation. As an illustration of these techniques, a novel lateral midair collision-avoidance maneuver is studied in an ideal setting, without accounting for the uncertainties of the physical reality. The challenges that naturally arise when applying such technology to industrial-scale applications is then detailed, and proposals are given on how to address these issues.