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Sep
24
awarded  Autobiographer
Feb
26
comment Formalizing “no junk, no confusion”
The Plus Transfrom gave a nearly equivalent english phrase; but the minus votes indicate an error somewhere...hmmm. "monotone" does also include formulas where every proposition is negative; however, I considered that presentation to be confusing junk, in a simple propositional formalism... I use monotone formulas for loop management in complex programs that solve QBFs; "correctness and clarity" are both of the utmost importance in such programs. Correctness is related to "no junk" and "clarity" allows code maintenance and improvements. Removing negation is standard treatment for me.
Feb
23
answered Formalizing “no junk, no confusion”
Feb
18
answered Cryptomorphisms
Jan
30
awarded  Teacher
Jan
29
revised The shortest path in first passage percolation
Far Corner variant of Midway. Edges length 1, zero fractions.
Jan
28
answered The shortest path in first passage percolation
Jan
25
answered Can you prove equivalence without being able to calculate it?
Jan
25
comment cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.
Aside about answering qbfs: any boolean formula P, given an order, has a related monotone formula Q, for correctly answering all 2^n quantifications of P. The size of Q is only well understood for 2cnfs and formulas that are already monotone. For 2cnf Ps, the size is identical to the size of (P + all resolutions). When P is already monotone, that Is the Q formula. I have not yet looked at variable swapping, for either 2qbfs, or for monotone formulas. Those two solvable cases would be a good place to begin to study variable swaps.
Jan
25
comment cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.
thank you darsh. I editted the original; question Two: Linear Corollary: Quantified monotone boolean formulas are linearly decidable. (hunting for any previous name) On importance: Equivalence between complexity classes, where few equivalences are known, is important. After good names are given, identitys become easier to apply. Variable order area is where future research lays. The Cardinal Equivalenece provides that the number of valid quantifications remains invariant after shuffling variables; but details about valid quantifications after any swap are a mystery.
Jan
22
revised cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.
simplified the question and presentation. Added corollary question.
Jan
21
awarded  Editor
Jan
21
revised cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.
added 3 characters in body
Jan
21
revised cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.
deleted 2 characters in body; edited tags
Jan
21
asked cardinal equivalence: for each boolean formula, |quantifications| = |assignments|.