Mathematical Structures in Computer Science


A modular formal semantics for Ptolemy  


a1 University of California, Berkeley, California, U.S.A. Email:;;;


Ptolemy is an open-source and extensible modelling and simulation framework. It offers heterogeneous modeling capabilities by allowing different models of computation, both untimed and timed, to be composed hierarchically in an arbitrary fashion. This paper proposes a formal semantics for Ptolemy that is modular in the sense that atomic actors and their compositions are treated in a unified way. In particular, all actors conform to an executable interface that contains four functions: fire (produce outputs given current state and inputs); postfire (update state instantaneously); deadline (how much time the actor is willing to let elapse); and time-update (update the state with the passage of time). Composite actors are obtained using composition operators that in Ptolemy are called directors. Different directors realise different models of computation. In this paper, we formally define the directors for the following models of computation: synchronous- reactive, discrete event, continuous time, process networks and modal models.

(Received August 23 2012)


  This work was partially supported by NSF project ExCAPE: Expeditions in Computer Augmented Program Engineering, and by the Center for Hybrid and Embedded Software Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards #0720882 (CSR-EHS: PRET) and #0931843 (ActionWebs), the U.S. Army Research Office (ARO #W911NF-11-2-0038), the Air Force Research Lab (AFRL), the Multiscale Systems Center (MuSyC) (which is one of six research centres funded under the Focus Center Research Program), a Semiconductor Research Corporation program and the following companies: Bosch, National Instruments, Thales and Toyota.