$L_2$ = {a,k | is a 3DNF (disjunctive normal form) and exist z such that safifies exactly k clauses in a} Validity of reduction $VC \leq_p L_2$

I have the following question :

$ L_2$ = {$ a,k$ | $ a$ is a 3DNF (disjunctive normal form) and exist $ z$ such that satisfies exactly $ k$ clauses in $ a$ }

I know that $ L_2 \in NPC$ .

Show that $ L_2 \in NP$ is relatively easy, I’ll skip that part.

I try to show that $ L_2 \in NPC$ using a reduction from $ VC \leq_p L_2$ (VC is vertex cover which we know in its $ NPC$ )

I defined the following function $ f$ :

$ $ f(G,k)=(a,k)$ $

I thought of something like that for each node $ i$ in $ G$ will define a literal $ x_i$ , and make it in $ 3DNF$ format, $ a=\bigvee(x_i \wedge x_i \wedge x_i)$ where $ 1 \leq i \leq n$ where $ n$ is the number of nodes in $ G$ . We can define that following $ z$ such that $ z$ safifies exactly $ k$ clauses, just give $ ‘1’$ literal $ x_i$ such that the node $ i$ is in the VC, and $ ‘0’$ otherwise, so such $ z$ exists.

So easy to see that $ (G,k) \in VC \implies (a,k) \in L_2$ since we showed explicitly such $ z$ that safifies exactly $ k$ clauses.

But I’m not sure the other side holds $ (G,k) \not\in VC \implies (a,k)\not\in L_2$ we given a graph that doesn’t have VC in size $ k$ but I think due to my building of a ($ a=\bigvee(x_i \wedge x_i \wedge x_i)$ ) we can find $ z$ that safifies exactly $ k$ clauses (actually we can find $ z$ that safifies $ x$ clauses where $ 1 \leq x \leq n$ where $ n$ is number of nodes in G.

So my reduction doesn’t hold?


Feather Fall Spell in 5E – Target Validity Issues?

Couldn’t find an answer to this in my reading of the source books nor on stackexchange. My players were engaged in an encounter in which enemies were able to manipulate air to "gust" them off a cliff. They did recognize that they needed to stay away from the edges but started to lose the battle because of pretty sour rolls. They decided they would leap from the cliff knowing that the sorcerer had the Feather Fall spell.

Feather Fall states: "Choose up to five falling creatures within range. A falling creature’s rate of descent slows to 60 feet per round until the spell ends. If the creature lands before the spell ends, it takes no falling damage and can land on its feet, and the spell ends for that creature."

Because of this targeting restriction, the spell could not be cast unless someone was already falling. As this takes a reaction, there seems to be no way to (prophylactically or otherwise) have the group under the spell if they all decided to jump in the same round of combat. In fact, it seems like it would take 5 castings (party of 5) over a series of 4 or 5 rounds to effect this strategy (with the sorcerer going last), which meant certain doom. I decided to call the session (it was time) to give me a little time to investigate this, but I basically told them there was no way I could see saving the party via feather fall. They were quite dejected considering they/he thought that Feather Fall could be cast as a proactive spell so that they could all jump safely on their own turn.

Can I confidently confirm that I have interpreted this right, whether RAW or RAI?

Certificates and keys validity

I’m connecting to a server via TLS. My device has installed server cert, device cert, private key and public key.

I read here validity SSL/TLS that TLS cert will last max 2 years.

This means that every 2 years I will have to updat all the certs stored into my device? Only server cert and device cert? Do I have to update also public and private key?

Validity of in-line help content over time as users graduate from novice to Intermediate stages

This is a question in regards to an Enterprise product.

Consider a selection menu –

Option 1

help text (2 liner max)

Option 2

help text (2 liner max)

Option 3

help text (2 liner max)

Notes –

1) This help text was added below the Options as there was feedback from new users that the Option Label itself was not sufficient to communicate the intent of the option.

2) Advanced users have come back saying that they do not need to see the help text every time as they are well aware of the options. This is very much understandable.

Questions –

Our product has both ends of the user expertise spectrum fairly distributed. Also, let’s note that users graduate overtime. A tooltip cannot be used as we have seen very less usage of the same and creates extra friction for new users, compared to immediate help. Considering that standard interaction design principles recommend designing for the ‘Intermediate User’ (Alan Cooper, Dan Normal) – is tooltip the only way out? Or are there other thoughts?

Please advice. Thanks!

Validity VFS301 Fingerprint scanner scans only once

I’ve searched countless forums about fingerprint scanner support with ubuntu, I’ve gotten the system settings to show the fingerprint login prompt. It lets you scan once, but after that it refuses to light up the scanner nor does it attempt a scan. There are no errors with fprint. I’m running 19.04, Here’s what it looks like in lsusb Bus 001 Device 003: ID 138a:0005 Validity Sensors, Inc. VFS301 Fingerprint Reader

How the validity of passport can affect transit between countries in South America?

I plan to fly to South America soon, the first country I plan to travel to is Argentina.

My plan is to have along trip that will involve traveling to other countries in the region.

My passport will expire in about 9 months.

Can I go from Argentina to a neighboring country (Chile) when my passport is less than six months away from the expiration date?

How do I extended the validity of a client certificate?

I have this script for creating a root and client certificate for azure point to site vpn connection.

I have extended the root certificate validity to 5 years but when I generate my client certificate it only had 1 year validity.

Here the powershell script I’ve used.


$  cert = New-SelfSignedCertificate -Type Custom -KeySpec Signature ` -Subject "RootCert-AzureP2SVPN" -KeyExportPolicy Exportable ` -HashAlgorithm sha256 -KeyLength 2048 ` -CertStoreLocation "Cert:\CurrentUser\My" -KeyUsageProperty Sign -KeyUsage CertSign -NotAfter(Get-Date).AddYears(5) 


New-SelfSignedCertificate -Type Custom -DnsName P2SChildCert -KeySpec Signature ` -Subject "ClientCert-AzureP2SVPN" -KeyExportPolicy Exportable ` -HashAlgorithm sha256 -KeyLength 2048 ` -CertStoreLocation "Cert:\CurrentUser\My" ` -Signer $  cert -TextExtension @("{text}") 

I have a valid B1/B2 Visa for US, but is its validity affected by a change of residence?

About 1,5 years ago, I got a B1/B2 visa—valid for 10 years.

I now moved to a different city within Germany.

The new city is entered in the password.

Is there any impact on the validity of my USA visa associated with it? Do I have to somehow forward my new contact details to the embassy?

Indian Passport nearing 6 months validity, Will it be a problem to travel to Australia without its renewal though a Valid 2yrs Visa is available

Passport expiring on 15th Dec 2019. Hold a WPLT for 2 years. Planning to travel Australia around 6th Jun 2019. Is there any 6 months restrictions on Indian passport in Australia, Will it be causing any issue with Immigration Services both during checks in India or Australia. Would like to get honest suggestion in this regards, Should I get my Passport renewed before travel only?