Abstract
Dioids, or idempotent semirings, are an algebraic structure that can be used to formally generate linear models for a class of timed discrete-event systems. A well-known example is the so-called max-plus algebra, which allows a linear representation of timed event graphs. This chapter will introduce basic notions of dioid theory, and will provide simple motivational examples. In particular, it will show how to generate compact models in a specific dioid, denoted by \(\mathcal{M}^{ax}_{in}[\gamma ,\delta] \); this is a quotient dioid in the set of formal power series in two variables with integer exponents and Boolean coefficients. This chapter will also discuss how to analyze important system aspects, such as the achievable throughput, in this framework. To demonstrate the usefulness of this approach for large real-world systems, it will be applied to High-Throughput Screening (HTS) problems, which have served as a benchmark within the DISC project.
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Brunsch, T., Raisch, J., Hardouin, L., Boutin, O. (2013). Discrete-Event Systems in a Dioid Framework: Modeling and Analysis. In: Seatzu, C., Silva, M., van Schuppen, J. (eds) Control of Discrete-Event Systems. Lecture Notes in Control and Information Sciences, vol 433. Springer, London. https://doi.org/10.1007/978-1-4471-4276-8_21
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