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There are a number of formal methods for distributed real-time systems in ubiquitous computing to analyze and verify the behavioral, temporal and the spatial properties of the systems. However most of the methods reveal structural and fundamental limitations of complexity due to mixture of spatial and behavioral representations. Further temporal specification makes the complexity more complicate. In order to overcome the limitations, this paper presents a new formal method, called Timed Calculus of Abstract Real-Time Distribution, Mobility and Interaction(t-CARDMI). t-CARDMI separates spatial representation from behavioral representation to simplify the complexity. Further temporal specification is permitted only in the behavioral representation to make the complexity less complicate. The distinctive features of the temporal properties in t-CARDMI include waiting time, execution time, deadline, timeout action, periodic action, etc. both in movement and interaction behaviors. For analysis and verification of spatial and temporal properties of the systems in specification, t-CARDMI presents Timed Action Graph (TAG), where the spatial and temporal properties are visually represented in a two-dimensional diagram with the pictorial distribution of movements and interactions. t-CARDMI can be considered to be one of the most innovative formal methods in distributed real-time systems in ubiquitous computing to specify, analyze and verify the spatial, behavioral and the temporal properties of the systems very efficiently and effectively. The paper presents the formal syntax and semantics of t-CARDMI with a tool, called SAVE, for a ubiquitous healthcare application.

Visual Representation of Temporal Properties in Formal Specification and Analysis using a Spatial Process Algebra