In “Elves of Evermeet”, how does the “construction” spell work?

This is in the 2nd edition book: Elves of Evermeet. On page 65 there is the description for a spell: Construction. Part of the description says:

The caster can create any object with a volume equal to 1,000 cubic feet (10x10x10 feet) per level. Each 1,000 cubic feet so created takes one entire day. Once created, the object can be added to at the same rate (1,000 cubic feet per day) for as long as the caster wishes.

This made me wonder, assuming a level 20 caster, how much volume can be created/added to in a day? Is it 1000 cubic feet/level, or only 1000, in which case, what is the point of mentioning the caster level?

Why can the construction of a polynomial-sized structure be done in logspace?

In paper the authors prove their problem is NL-complete. At some point in their proof however, they construct a polynomial-sized graph, and state this can clearly be done in logspace, which is not that clear to me. It would seem to me that constructing a polynomial-sized graph would only be doable with polynomial space, since how would one store the constructed graph with less space? The wikipedia page on logspace reductions tries to clear up this misunderstanding by stating

It is possible that such a machine may not have space to write down its own output, so the only requirement is that any given bit of the output be computable in log-space.

which somewhat helps. I’m still missing the intuition behind it though, and am searching for an intuitive example of why the construction of some polynomial-sized structure can “clearly” be done in logspace.

Determining Attribute Flow Compiler Construction

I am trying to determine how to actually answer these questions in my textbook. I have 3 questions which is as stated below.

These questions, i do not quite understand what the uparrow and downarrows have to do with the attribute flow and definition of this grammar.

For each of the following grammar indicate whether overall, general attribute value flow is bottom-up, top-down, left-to-right, and right-to-left.    (a).          G -> A(downarrow)l          A(downarrow)n -> B(downarrow)3n A(downarrow)7n          ->”c” C(downarrow)n-1          B(downarrow)n -> ”a” B(downarrow)n+4 “b” C(downarrow)2n          -> ”b”          -> ”c”        (b)         G -> A(uparrow)x          A(uparrow)n -> B(uparrow)u (uparrow)v  A(uparrow)y        [x=uy+v]          -> ”c” C(uparrow)z                                        [x=2z]          B(uparrow)v -> ”a” B(uparrow)r(uparrow)s“b” C(uparrow)x   [u=2r+x-s; v=s+1]          -> ”b”                                                    [u=1; v=2]          C(uparrow)x  -> ”c”                                       [x=3]   (c)          G -> A(downarrow)0(uparrow)r          A(downarrow)x(uparrow)z -> B(downarrow)y (uparrow)z  A(downarrow) x(uparrow)y                            -> ”c”  C(downarrow)x(uparrow)y                                       [z=10y+3]          B x w -> “a” B(downarrow)10y+2(uparrow)z “b” C(downarrow)x(uparrow)y  [w=10z+1]          -> ”b”                                                                [w=10x+2]          C x y -> ”c”                                                         [y=10x+3] 

Is Certification path construction algorithm needed for SSL/TLS?

In the TLS Handshake a Certificate message is sent. This message contains the (chain of) certificates needed to validate the provided certificate of the communicating party.

However, I have also read some papers, and also defined in RFC5280, that the certification path process is challenging; and, an algorithm is needed to actually do the path construction.

This confused me, since during the TLS Handshake the chain of trust is provided in the Certificate message. Therefore I was wondering: Is a Certification path algorithm also needed in the TLS protocol?

  • If so, why is it needed? As far that I know, the Certificate message sends all the certificates in the chain of trust.
  • If not, is it true then that the Certificate message does not (always) provide all the certificates in the chain? Or maybe, does the certification path algorithm not apply at all for SSL/TLS; but for what kind of protocols is it needed then?

Complexity of k-ary tree construction

I have the following task: Suppose we have an algorithm that partitions a set of n inputs using a perfect k-ary tree where each node takes linear time to construct based on the number of inputs to the node. Give the complexity for constructing the entire tree based on the arity and the initial input.

My idea:

Constructing the root is $ \mathcal{O}(n)$ . The $ k$ children have $ k *\mathcal{O}(\frac{n}{k})$ , the next layer $ k^2 * \mathcal{O}(\frac{n}{k^2})$ and so on. Now I considered $ k$ a constant and get $ \mathcal{O}(n)$ as a final result, cause $ \mathcal{O}(n) + \mathcal{O}(n) = \mathcal{O}(n)$ . But that seems awfully easy and that’s never a good sign x). Someone can elaborate/revise?

How To Process Construction Waste?

Environmental protection is the primary issue in the modern industry. Especially for the mechanic’s manufacturers, the construction waste portable rock crusher machine makes the waste of urban buildings turn waste into treasure, and reuse is one of the important goals of the development of environmental protection in the world. Today, the waste from the construction site is very large. The portable rock crusher machine can handle the construction waste with its excellent performance. Here are some advantages of the portable rock crusher manufactured by HXJQ. 1. The waste bricks are used for building aggregates after being crushed by the portable rock crusher plant. The partition wall plate is not only light and high in strength but also soundproof and small, which greatly reduces the cost of the plate due to the easy-access and cheap material. 2. After the brick, stone, concrete, and other scraps are being crushed, they can be used for sand and laying mortar, etc. After the finely crushed concrete blocks mixed with the standard sand, the fine aggregate is used for wall plastering, paving tiles, etc. 3. The recycled bricks that processed by the HXJQ portable rock crusher plant are more than 100 types, all of which have various performance indicators. 4. After the scrap concrete block is crushed, it can be used as aggregate in concrete cast-in-place or prefabricated components for non-bearing parts of buildings. This not only saves construction funds but also does not reduce the strength of the structure.

How do areas where construction has replaced nature affect the spell Commune with Nature’s ability to give information on buildings?

One of the limitations of Commune With Nature is that

The spell doesn’t function where nature has been replaced by construction, such as in dungeons and towns.

I am uncertain what that entails given that one of the subjects one can divine is buildings.

Baker, Gill, Solovay – construction of oracle B such that P^B != NP^B

I have some questions about Baker, Gill, Solovay proof of the existence of an oracle such that P^B != NP^B. The proof can be found in Siam Journal of Computing, 4:432-442, 1975 [219].

  • Why Isn’t this construction considered a counterexample to P = NP? And if it is not, can it be strengthened into one? It seems tome that we have constructed a languge recognizable in NP time but not in P time.

  • In the proof there is the sentence “If P_i^B(i) accepts 0^n, then place no string into B at this stage.” How can this possibly happen?

I figured that, since B is intially empty, the oracle B(i) ALWAYS rejects. So the only reason why P_i would accept is some reason OTHER than a question to B(i). Please correct me if I am wrong.

The proof in question is verbatim reproduced here. The original paper is here.