Formalization of a realtime person-computer ensemble system with an effective matching algorithm

A person-computer ensemble system is one of time concerned cooperative systems, which performs secondo (the second part) in an ensemble played by a computer-controlled piano cooperating with primo (the leading part) played by a person performer. This is a good example of intelligent realtime programs appropriate for formal verification and analysis. NΣ-labeled calculus is a formal system in order to describe such systems including time-concerned recognition, knowledge, belief and decision of persons or computer programs together with related external physical or logical phenomena. In the realtime performance of music, to determine which key is played just now by the person performer, the matching algorithm between the score and the realtime input from the person performer is important. If there are some mistouching, i.e. playing an incorrect key, or other mistake, error, etc., and if the program does not detect and correct such errors, it does not determine which note is performed just now and which note of the secondo will be done just after now, and hence, it cannot control the performance speed. Therefore, the matching method including correction of these mistouches is essential. A simple but very efficient matching method with error detecting has been already developed and presented by the authors. In this paper, the formal representation of the program and its formal specification satisfied by the program written and verified in the calculus are introduced.