@inproceedings{vJ11,

title = {Synthesizing Systems with Optimal Average-Case Behavior for Ratio Objectives },

author = {von Essen, Christian and Jobstmann, Barbara},

year = {2011},

booktitle = {International Workshop on Interactions, Games and Protocols},

publisher = {Electronic Proceedings in Theoretical Computer Science},

team = {DCS},

abstract = { We show how to automatically construct a system that satisfies a
given logical specification and has an optimal average behavior with
respect to a specification with fractional costs.
When synthesizing a system from a logical specification, it is often
the case that several different systems satisfy the specification.
In this case, it is usually not easy for the user to state formally
which system she prefers. Prior work proposed to rank the correct
systems by adding a quantitative aspect to the specification. A
desired preference relation can be expressed with (i) a quantitative
language, which is a function assigning a value to every possible
behavior of a system, and (ii) an environment model defining the
desired optimization criteria of the system, e.g., worst-case or
average-case optimal.
In this paper, we show how to synthesize a system that is optimal
for (i) a quantitative language given by an automaton with a
fractional cost function, and (ii) an environment model given by a
labeled Markov decision process. The objective of the system is to
minimize the expected (fractional) costs. The solution is based on
a reduction to Markov Decision Processes with extended-fractional
cost functions which do not require that the costs in the
denominator are strictly positive. We find an optimal strategy for
these using a fractional linear program. },

}