  For deterministic and probabilistic programs we investigate the problem of
program synthesis and program optimisation (with respect to non-functional
properties) in the general setting of global optimisation. This approach is
based on the representation of the semantics of programs and program fragments
in terms of linear operators, i.e. as matrices. We exploit in particular the
fact that we can automatically generate the representation of the semantics of
elementary blocks. These can then can be used in order to compositionally
assemble the semantics of a whole program, i.e. the generator of the
corresponding Discrete Time Markov Chain (DTMC). We also utilise a generalised
version of Abstract Interpretation suitable for this linear algebraic or
functional analytical framework in order to formulate semantical constraints
(invariants) and optimisation objectives (for example performance
requirements).
