  We present $\textit{Probabilistic Total Store Ordering (PTSO)}$ -- a
probabilistic extension of the classical TSO semantics. For a given
(finite-state) program, the operational semantics of PTSO induces an
infinite-state Markov chain. We resolve the inherent non-determinism due to
process schedulings and memory updates according to given probability
distributions. We provide a comprehensive set of results showing the
decidability of several properties for PTSO, namely (i) Almost-Sure (Repeated)
Reachability: whether a run, starting from a given initial configuration,
almost surely visits (resp. almost surely repeatedly visits) a given set of
target configurations. (ii) Almost-Never (Repeated) Reachability: whether a run
from the initial configuration, almost never visits (resp. almost never
repeatedly visits) the target. (iii) Approximate Quantitative (Repeated)
Reachability: to approximate, up to an arbitrary degree of precision, the
measure of runs that start from the initial configuration and (repeatedly)
visit the target. (iv) Expected Average Cost: to approximate, up to an
arbitrary degree of precision, the expected average cost of a run from the
initial configuration to the target. We derive our results through a nontrivial
combination of results from the classical theory of (infinite-state) Markov
chains, the theories of decisive and eager Markov chains, specific techniques
from combinatorics, as well as, decidability and complexity results for the
classical (non-probabilistic) TSO semantics. As far as we know, this is the
first work that considers probabilistic verification of programs running on
weak memory models.

Programming Languages;Hardware Architecture