Continuous mathematics and formal language theory
Lamine commented on the connection to the Chomsky-Schützenberger enumeration theorem. Recently, a few research problems in formal language theory were solved using continuous mathematics via this connection. For example:


Hermann Gruber, Jonathan Lee, and Jeffrey Shallit. Enumerating Regular Expressions and their Languages. available online at arxiv.org as arXiv:1204.4982, 2012
Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis:
A Hitchhiker's Guide to descriptional complexity through analytic combinatorics. Theor. Comput. Sci. 528: 85-100 (2014)
Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis:
Average Size of Automata Constructions from Regular Expressions. Bulletin of the EATCS 116 (2015)
Rafaela Bastos, Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis:
On the Average Complexity of Partial Derivative Automata for Semi-extended Expressions. Journal of Automata, Languages and Combinatorics 22(1-3): 5-28 (2017)


The first two of the above references also give a survey of the mathematical and/or historical background.