A Modular Visual Model for Hybrid Systems RaduGrosu,ThomasStauner ⋆ andManfredBroy Institut f¨ ur Informatik, TU M¨ unchen, D-80290 M¨ unchen Email: {grosu,stauner,broy}@informatik.tu-muenchen.de Abstract. Visual description techniques are particularly important for the design of hybrid systems because specifications of such systems must usually be discussed between engineers from a number of different disci- plines. Modularity is vital for hybrid systems not only because it allows to handle large systems, but also because hybrid systems are naturally decomposed into the system itself and its environment. Based on two different interpretations for hierarchic graphs and on a clear hybrid computation model, we develop HyCharts, two modular vi- sual formalisms for the specification of the architecture and behavior of hybrid systems. The operators on hierarchic graphs enable us to give a surprisingly simple denotational semantics for many concepts known from statechart-like formalisms. Due to a very general composition oper- ator, HyCharts can easily be composed with description techniques from other engineering disciplines. Such heterogeneous system specifications seem to be particularly appropriate for hybrid systems because of their interdisciplinary character. 1 Introduction Hybridsystemshavebeenaveryactiveareaofresearchoverthepastfewyears andanumberofspecificationtechniqueshavebeendevelopedforsuchsystems. Whiletheyareallwellsuitedforclosedsystems,thesearchforhybriddescription techniquesforopensystemsisrelativelynew. Foropensystems–aswellasforanylargesystem–modularityisessential. It is not only a means for decomposing a specification into manageable small parts,butalsoaprerequisiteforreasoningaboutthepartsindividually,without havingtoregardtheinteriorofotherparts.Thus,itgreatlyfacilitatesthedesign processandcanhelptopushthelimitsofverificationtools,likemodel-checkers, further. With a collection of operators on hierarchic graphs as tool-set, we follow theideasin[6]anddefineasimpleandpowerfulcomputationmodelforhybrid systems.BasedonthismodelHyCharts,namelyHySChartsandHyACharts,are introducedastwodifferentinterpretationsofhierarchicgraphs.HySChartsarea visualrepresentationofhybrid,hierarchicstatetransitiondiagrams.HyACharts areavisualrepresentationofhybriddata-flowgraphs(orarchitecturegraphs) and allow to compose hybrid components in a modular way. The behavior of ⋆ The second author was supported with funds of the DFG, within the priority program Design and design methodology of embedded systems (reference number Br 887/9-1).