A bstract The string vertices of closed field theory are subsets the moduli spaces punctured Riemann surfaces that satisfy a geometric version Batalin-Vilkovisky master equation. We present homological proof existence and their uniqueness up to canonical transformations. Using hyperbolic metrics on with geodesic boundaries we give an exact construction as sets systole greater than or equal L ≤ ...

The consensus string (or center string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. It is well-known that the consensus string problem for a finite set of equal-length strings is NP-complete. We study the consensus string problem for multiple regular languages. We define the consensus string of languages L1, . . . , Lk to be wit...