Abstract
We show how recent results concerning quantitative forms of automata help providing refined understanding of the properties of a system (for instance, a program). In particular, combining the size-change abstraction together with results concerning the asymptotic behavior of tropical automata yields extremely fine complexity analysis of some pieces of code.
This abstract gives an informal, yet precise, explanation of why termination and complexity analysis are related to automata theory.
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Notes
- 1.
Though we take the principle, we do not use the standard notation of max-plus automata, which are traditionally defined as automata weighted over the max-plus semiring.
- 2.
In the standard terminology, non-costly transitions would be given weight 0, while costly ones would be attributed weight 1.
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Colcombet, T., Daviaud, L., Zuleger, F. (2017). Automata and Program Analysis. In: Klasing, R., Zeitoun, M. (eds) Fundamentals of Computation Theory. FCT 2017. Lecture Notes in Computer Science(), vol 10472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55751-8_1
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