Propositional logic is intractable; there are forms that take too much time to reduce, no matter how clever your axioms and algorithms are. There has been a great deal of academic work identifying what is hard and what is easy, mostly centered around tautology identification, finding forms without meaningful variables.

Virtual insertion is an exotic boundary logic decision procedure and minimization algorithm that further generalizes the central ideas of Pervasion and transparency. It permits the postulation of void-equivalent forms that catalyze reduction while not actually being present.

The first monograph is a comprehensive discussion of how Losp (my implementation of boundary logic) addresses complexity in parens forms. It shows which parens forms are easy, and ends with several intractable forms that reduce using virtual insertion.

The following pieces contributed to the Computational Complexity monograph, with some redundancy. They progress from void-based extensions of Pervasion, through the use of virtual insertion on intractable forms, to the decomposition and analysis of complex problems.