### November 19, 2018

**Valentina Castiglioni**(LIX - Ecole Polytechnique)

When probabilistic aspects of process behavior are taken into account, reason-

ing in terms of behavioral equivalences is only partially satisfactory: any tiny

variation in the values of the probabilities, which may be also due to a measure-

ment errors or approximations, will break process equivalence without giving

any further information on the differences in their behaviors. For this reason,

behavioral metrics have been proposed. The idea is to define, for each semantics,

a proper notion of distance on processes allowing us to quantify the differences

in the behavior of processes with respect to that particular semantics.

However, the interplay of nondeterminism and probability, typical of prob-

abilistic automata, leads to several possible expressions for process behavior,

thus making the definition of a proper metric subject to interpretations.

In this talk, we will discuss this issue by considering linear properties only.

In detail, we will present three main approaches to probabilistic trace seman-

tics: the trace distributions, the trace-by-trace and the supremal probabilities

approaches. For each of them we will propose a notion of trace metric, mea-

suring the disparities in the linear behavior of processes, and we will compare

these metrics with respect to their properties and their distinguishing power.