  The simplified linguistic relation between syntax and semantics as intrinsic
property of classic Arabic motivates a dedicated look at P vs. NP in light of
efforts and solutions presented by ancient Arab- and Muslim scholars to
facilitate logical- and mathematical deduction. In Islamic Jurisprudence (Fikh)
it has recently been shown [Abdelwahab et al. 2014] that if a formal system
expressing Fikh is chosen in such a way that it is both, logically complete and
decidable, the question of a complete and consistent legislation is decidable.
If this formal Fikh-system is additionally chosen to be at least as expressive
as propositional logic, the deduction of detailed sentences is efficient while
the deduction of general rules is NP-complete. Further investigation reveals
that ancient scholars adopted a very efficient approach for checking the
validity of assertions with regard to both, language and logical argument which
was mainly characterized by the extensive use of syntactical patterns already
existent in input-variables. Accordingly, this paper introduces efficient
pattern-oriented procedures for 3-SAT as well as 2-approximation algorithms for
MinFBDD. It opens up the possibility of constructing polynomial sized FBDDs for
all Boolean functions expressed in a compact way. Eventually, an application of
this new 3-SAT-solver is shown to enable polynomial upper bounds of the number
of nodes in FBDDs constructed for finite projective planes problems overhauling
the currently known exponential lower bounds.
