An algebraic approach to equivalence of MSO transductions of graphs of bounded treewidth

We prove MSO-transductions of graphs of bounded treewidth have decidable 
equivalence modulo fractional isomorphism with real coefficients (not necessarily nonnegative).
The main goal of this talk is to present a new approach to equivalence problem of MSO-transductions of graphs of bounded treewidth.
This approach relies on associating to a graph a list of polynomials or generating functions
which can be updated by a polynomial function after join and forget operation of sourced graphs.

This is joint work with Mikołaj Bojańczyk.