Matrix interpretations can be used to bound the derivational
and runtime complexity of term rewrite systems. In particular,
triangular matrix interpretations over the natural numbers are known
to induce polynomial upper bounds on the complexity of (compatible)
rewrite systems. Recently a couple of improvements were proposed,
based on the theory of weighted automata and linear algebra. In this
talk we focus on the application of weighted automata theory on the
runtime complexity analysis of rewrite systems and clarify the
connection to joint spectral radius theory.
The talk is based on joint work with Aart Middeldorp, Friedrich
Neurauter, Johannes Waldmann, and Harald Zankl.