Istituto di Scienza e Tecnologie dell'Informazione     
Bortolussi L., Sanguinetti G. Learning and designing stochastic processes from logical constraints. In: QEST 2013 - Quantitative Evaluation of Systems. 10th International Conference (Buenos Aires, Argentina, 27-30 August 2013). Proceedings, pp. 89 - 105. Kaustubh Joshi, Markus Siegle, MariŽlle Stoelinga, Pedro R. DíArgenio. (Lecture Notes in Computer Science, vol. 8054). Springer, 2013.
Continuous time Markov Chains (CTMCs) are a convenient mathematical model for a broad range of natural and computer systems. As a result, they have received considerable attention in the theoretical computer science community, with many important techniques such as model checking being now mainstream. However, most methodologies start with an assumption of complete specification of the CTMC, in terms of both initial conditions and parameters. While this may be plausible in some cases (e.g. small scale engineered systems) it is certainly not valid nor desirable in many cases (e.g. biological systems), and it does not lead to a constructive approach to rational design of systems based on specific requirements. Here we consider the problems of learning and designing CTMCs from observations/ requirements formulated in terms of satisfaction of temporal logic formulae. We recast the problem in terms of learning and maximising an unknown function (the likelihood of the parameters) which can be numerically estimated at any value of the parameter space (at a non-negligible computational cost). We adapt a recently proposed, provably convergent global optimisation algorithm developed in the machine learning community, and demonstrate its efficacy on a number of non-trivial test cases.
URL: http://link.springer.com/chapter/10.1007%2F978-3-642-40196-1_7
DOI: 10.1007/978-3-642-40196-1_7
Subject Markov Chains
B.8.2 Performance Analysis and Design Aids

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