  Motivated by string field theory, we explore various algebraic aspects of
higher spin theory and Vasiliev equation in terms of homotopy algebras. We
present a systematic study of unfolded formulation developed for the higher
spin equation in terms of the Maurer-Cartan equation associated to differential
forms valued in L-infinity algebras. The elimination of auxiliary variables of
Vasiliev equation is analyzed through homological perturbation theory. This
leads to a closed combinatorial graph formula for all the vertices of higher
spin equations in the unfolded formulation. We also discover a topological
quantum mechanics model whose correlation functions give deformed higher spin
vertices at first order.
