Operator algebras for higher rank analysis and their application to factorial languages

We study strong compactly aligned product systems of ℤ + over a C*-algebra A. provide description their Cuntz-Nica-Pimsner algebra in terms tractable relations coming from ideals This approach encompasses where the left action is given by compacts, as well wide class higher rank graphs (beyond row-finite). Moreover we analyze factorial languages and C*-algebras. Many one results literature find here analogues. In particular, show that sofic language coincides with Cuntz-Krieger its unlabeled follower set graph. However, there are also differences. For example, can lie in-between first quantization quotient supported operators.