Fragments of themes

You see, when I began developing my axioms, I was not sure that they would work in every instance; the language was created to be simple ensuring flexibility and strong syntactical witnessing features.

One particular instance deals with querying a combinatorial space oracle, for the extent we will refer to this as an EXPSPACE oracle. This space contains k disjunctive strings of all permutations of particular set of n objects, with the relationship k = 2^n.

Now say with a complement of this set of n objects we construct an expression, it may take on many forms, for the time being we will concentrate on nSAT, this expression can be represented in CNF, just as our full EXPSPACE. Although by the complement, we have that binding of sites will not occur until execution.

This is where the problem gets interesting. Suppose that we construct both an EXPSPACE and nSAT, composed of L and complement(L), respectfully; and these two will decide on themselves by the syntax of the construction of the objects and ultimately by the physical description of the complement function. We are posed with the question: If one of these strings from nSAT meets with its corresponding satisfying member, what would stop the small bit length from going to where a larger bit length string could have obtained a stronger satisfiability assignment, (of course we assume that a small bit length has lesser degree of conjunctions than a string with a larger bit length, this may not be true in an application!).

So I consider the cases:
(Case 1): It does not make a difference, you are querying an oracle, it should have the same output regardless.
(Case 2): It does make a difference, the longer strings should have priority, allowing for shorter assignments to take places at a later iteration in the runtime.

Both cases are promising, and (Case 1) is favorable, but (Case 2) remains practical; as O(case1)=1 and O(case2)=k.
I remain to contemplate the consequences...