np complete – Concrete example for reducing vertex cover to subset sum

In computer-aided infectivity, we often come across the need to reduce the vertex cover (VC) problem to a subset sum problem …

We do

… mainly to prove that Subset Sum is NP-Complete.

There is no particular reason to go this way. Karp (1) defined the Knapsack problem as: $ a_1, dots, a_r, b in mathbb {Z} $is there a sentence $ S subseteq {1, dots, r } $ so that $ sum_ {i in S} a_i = b $? This is a variant of the sum now called subset. If you prefer to define the subset Sum so that $ b $ is always zero, we'll come back to it soon.

Karp shows that Subset is Sum NPcompletely through the chain of reductions
$$ text {SAT} leq text {3SAT} leq text {Chromatic Number} leq text {Exact Coverage} leq text {Subset} ,. $$
In particular, reducing Exact Cover to Subset Sum creates an instance where the $ a_i $and $ b $ If all are positive, you can specify whether the subset "Is there a subset whose sum is zero?" should be defined $ a_ {r + 1} = – b $,

Because Subset Sum and Vertex Cover are both NPIn full, there is clearly a reduction between them. However, you should not expect that there will be a "nice" reduction in which a small VC instance naturally transforms into a small subset-sum instance where you say, "Aha, now I understand." And that goes for most pairs of NP-complete problems. In complexity theory classes, we teach simple, intuitive reductions, usually between problems that somehow resemble each other, or between SAT or 3SAT and a problem that is not Boolean formulas. This can give the impression that there is a natural reduction between each pair of NP-complete problems; In fact, there is usually no.

(1) Richard M. Karp, Reducibility in combinatorial problems, in the Complexity of computer calculations, Plenary Press, 1972. (PDF)

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Enter image description here

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How much of the system will cover the safe start?

Background: We're developing for a Debian 9.8 system, but the space we work in is dominated by embedded devices.

According to Wikipedia, Secure Boot can "secure the boot process by preventing the loading of drivers or operating system loaders that are not signed with an acceptable digital signature." By that I mean that code is protected at the kernel level, but not user-level code.

I have some terminology issues with my boss who feels that Secure Boot can protect the entire operating system. I believe that Secure Boot can only back up the entire system if the computer in question is an embedded device (you will never receive any software updates, so you can group all the executables together and sign them). If the device is a typical PC, starting it safely can not provide security (your PC is constantly being updated with software, which means that an executable block is constantly changing and you need to recalculate / sign it entire block with each update).

Am I right or is he? Is there an easy way to extend Secure Boot's protection to our custom user-level software? Is there anything similar to Secure Boot that I should look out for to secure user-level software?

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