CNF2 = { φ | φ is a satisfiable CNF-formula in which each variable appears at most 2 times}. Show CNF2 is in P


CNF2 = { φ | φ is a satisfiable CNF-formula in which each variable appears at most 2 times}. Show CNF2 is in P.

I found this solution:

We use the method of resolution to take the variables out one by one. First, observe that if the variable x appears only as x or only as ¬x in the formula, or if it appears only once, we can satisfy whatever clauses it takes part of and thus exclude x and these clauses. On the other hand, if x and ¬x are both clauses for some variable, we know our formula is not satisfiable. So the interesting case is when we have x in one clause, c+, and ¬x in another, c−, such that (c+, c−) 6= (x, ¬x). Call the remaining part of the formula r. We claim that c+ ∧ c− ∧ r is satisfiable if and only if c ∧ r is satisfiable, where c is the disjunction of all literals from c+ and c− that are not x or ¬x. Indeed, given a satisfying assignment of c+ ∧ c− ∧ r, some literal in either c+ or c− has to be satisfied, because we can’t have both x and ¬x be satisfied. Thus, forgetting the assignment of x, we get a satisfying assignment of c ∧ r. Conversely, given a satisfying assignment of c ∧ r, some literal different from x and ¬x will be satisfied in either c+ or c−; the other one can be satisfied by assigning x in an appropriate way. Thus, we have a procedure to decide satisfiability of a CNF2 formula φ efficiently: reduce the number of variables by the methods described above; if there is no contradiction along the way and you get to the empty formula, then φ is satisfiable. Otherwise, it is not.

Why is there not a control about to check if each variable appears at most 2 times?

Deliver Your Direct Mail Campaign With Impact by Using Variable Data Printing

Variable Data Printing (VDP) by means of definition, is a form of on-call for printing that attracts records from a particular database, to personalize text and photographs from one printed piece to the following, without preventing or slowing down the printing method.

Sounds like a mouthful, but actually a easy concept whilst it comes down to it.

VDP isn’t always a new concept. It has been round for just over a decade but growing in popularity as marketers search for approaches to supply their junk mail campaigns with most effect.

With VDP, entrepreneurs are able to customize their Latest mailings database in lots of distinctive ways. The maximum easy and famous shape is personalizing the salutation (i.E. Dear Mary). As era advances, alternatives are evolving and the capability to customize will become even greater complex. Now you could….
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• Assign unique promotional codes to sure businesses
• Personalize offers to a selected demographic
• Apply personalised URLs (purls)
• Customize your message primarily based upon past purchases and prediction of destiny needs
• Personalize snap shots (i.E. “Mary” written in an photograph of clouds, a sandy seashore, a constructing, a avenue signal, etc.)

Really, the options have grow to be infinite.

The cutting-edge fashion in variable facts printing today is a method called Door-to-Door Mapping. The call can’t do it better justice; door-to-door mapping provides instructions from the “front door” of the receiver to a destination distinctive by using the sender.

With both B-to-B and B-to-C opportunities, door-to-door mapping offers the closing in ease of response in direct mail campaigns. As the sender, you aren’t simplest handing over a excessive impact message, but now you are making it that a great deal easier for the target audience to reply in your provide by way of giving them directions for your occasion. An ideal application for door-to-door mapping is an occasion invitation.

Here are a few industries in order to gain by the use of door-to-door mapping, and examples of uses:

• Healthcare…..New affected person recruiting by means of a new pressing care center
• Real Estate…..Open residence invite
• Education…..Freshman elegance orientation or alumni event
• Manufacturing…..New product demonstration or manufacturing unit excursion
• Financial/Banking…..Invitation to an estate planning seminar
• Casino…..Entice out of state “excessive rollers”
• Ad organizations…..Invitation to “dealer day” occasion
• Restaurant…..New place announcement and coupon provide
• Non Profit Agencies…..Invitation to fund elevating gala

While door-to-door mapping can produce splendid reaction charges, being a tremendously unique and personal shape of variable facts printing, the important thing to attaining success lies inside the agency’s capability to devise in advance. Segmenting your database and maintaining contemporary records will can help you re-marketplace your data for greater effect. Although time eating, it’s far well really worth it ultimately.

In a era pushed by technological advances, alternatives for junk mail will best keep growing and trade, just as we have visible with the beginning of door-to-door mapping. The strengths and blessings of utilising VDP in direct mail campaigns are enormous but the backside line that marketers need to recall is: the higher the impact, the greater the reaction.

Problem of code Linkedlist while using struct variable

Code for linkedlist using memory allocation:https://ideone.com/loH6Ev.

Code for linkedlist using struct variable:https://ideone.com/YrZmW9. When i use 2nd code it doesn’t work correctly.It print just two value.In while loop of create() i use struct node type variable declaration.that’s why it should it would declare a new struct node type link variable and a new memory(struct node link) address should be seen in every execution .So what’s the problem?I am a newbie learning data structure using c.Please explain in simple language. Thank you sir.

Coding the Javascript part of a TinyMCE plugin: the IDE can’t resolve the tinymce variable

I’ve copied a very basic plugin for WordPress which adds a button to TinyMCE.

The code is correct and works. But while I’m coding (in PHPStorm), the IDE can’t resolve the javascript objects. How can I configure PHPStorm (or a generic IDE) to see the code of TinyMCE included in WordPress?

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How does a variable caster level work for spells?

There are a fair few spells that have more powerful results with a higher Caster Level. Magic Missile creates more missiles, Fireball uses more damage dice, Cure spells restore more hitpoints, etc. In addition, any spell that can be resisted/countered/dispelled uses Caster Level to determine how likely this is to happen.

But I’m unclear where exactly this caster level comes from. Lets take Magic Missile as our example. It is a first level spell, so as a level one wizard I can prepare it in a first level spell slot just fine. But once I become a fifth level Wizard, get a caster level of three and have access to third level spell slots, I’m not sure what happens.

If I prepare Magic Missile in a first level spell slot, does it get its second missile because I personally have Caster Level three, or does the spell itself need to be in a third level spell slot to be considered a Caster Level three spell? Or is it some third thing I’m just unclear on?

Are polynomials in one variable logspace-computable?

Given a polynomial function $ $ p\quad=\quad \lambda\, x\in\mathbb{N}_0.\ \sum_{i=0}^n a_i x^i$ $ with $ a_i\in\mathbb{Z}$ for all $ i\leqslant n$ , can you compute $ p$ by a logspace transducer if the input and the output are in binary, the working tape is semi-infinite, and there are no stationary N rules (i.e., all the transducer rules are either L (move left) or R (move right) rules)?