Abstract
In this chapter, we present the dimensions of the time modeling problem. Despite its intuitive evidence, the mathematical modeling of time has produced highly diversified approaches and notations. The dimensions presented in this chapter will guide their presentation and comparison throughout the following chapters. A first basic dimension is whether the domain adopted to describe time is discrete or dense. A second dimension distinguishes whether the time domain is only ordered or is provided with a metric. A third dimension separates linear time domains from branching ones. Then, we distinguish between deterministic, nondeterministic, and probabilistic system models; we discuss the problem of formalizing time progress; we introduce the issue of modular composition and its impact on timing analysis.
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Notes
- 1.
A property is decidable if there exists an algorithmic procedure that can determine, in finite time, whether the property holds in any given system model; otherwise, it is undecidable. Chapter 6 introduces the notion with more precision for readers unfamiliar with the theory of computability.
- 2.
The following three sentences refer to some real historical facts mentioned in Alessandro Manzoni’s The Betrothed; the dates and figures are plausible but not necessarily accurate.
- 3.
This quotation is usually attributed to Abraham Lincoln, but this is allegedly apocryphal.
- 4.
Circa 490–425 B.C.
- 5.
Kilkenny, 1685–Oxford, 1753.
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Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M. (2012). Dimensions of the Time Modeling Problem. In: Modeling Time in Computing. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32332-4_3
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