2017, Adithya Murali’s internship

Adithya Murali worked on the small category of deterministic matrices: the vertices are the pairs (p,q) of natural integers, the arrows from p to q are matrices of languages such that each row is a q-tuple of pairwise disjoint languages, whose union is a prefix-language.

Though this algebraic structure has already been used in several works in formal language theory, a systematic study is still lacking. Along these lines, Adithya Murali has:
– expanded a sketchy manuscript of the supervisor into a firm formal framework,
– increased the knowledge on equations in this structure, namely by making sound an interesting finiteness result on equations (the shears lemma) and contributing to its proof.

This work, though not finished, will constitute a research-report.