Decoding manchester line coding to original signal - networking

Sorry for this homework type question,but I have been trying this question since long,and I haven't got an approach in my head.
I have tried searching the internet for line decoding (the opposite of line encoding),but haven't got any appreciable results. Can anyone help?

Related

2D Raycasting/Checking if 2 line segments intersect

How would I make a 2D raycast? Also, how would I check if 2 line segments intersect (relativity the same thing in my eyes, probably different though). I am not using unity or anything, I am just using plain python (I can translate from most languages to python so I don't really care what language you use) and don't want to use a library so I can learn. But every article I look at has no actual explanation, it just shows code. I've looked at the Geeks4Geeks one and that also really only shows code and does not explain what it does. So if someone could explain it that would be helpful.

what happens to Schweizer T-Norm when p goes to zero?

I am reading Jang's book of Neuro-Fuzzy and Soft Computing and in the 2nd chapter the author talks about Schweizer and Sklar T-Norm which is presented by this equation:
it's a handy T-norm. in the exercises (#20 page 45) it asks what would happen to the Tss(a,b,p) if p->0
In fact it asks to show that the whole equation is going to be just ab in the end.
I tried different things and at last, I used Ln but I got this: -1/p Ln(a^-p + b^-p) and I have no idea where to go from here!
can anybody suggest anything? thanks for your help.
p.s: is there any simple way of expanding Ln(x+y) generally?

Math ML MO uses

What do following snippets of code do in Math ML files? I removed those lines and it still worked fine for me.
<mo>⁡</mo>
<mo>⁢</mo>
<mo></mo>
Answering to any of them or just letting me know what they are would be very much appreciated.
The first two are ⁡ function application and ⁢ invisible times. They help indicate semantic information, see this Wikipedia entry
The last one, , could be anything since it lies in the Unicode Private Use Area which is provided so that font developers can store glyphs that do not correspond to regular Unicode positions. (Unless it's a typo and really 6349 in which case it's a a Han character.)

Recursion Problems in Prolog

I'm having some difficulties in prolog, I'm trying to write a predicate that will return all paths between two cities, although at the moment it returns the first path it finds on an infinite loop. Not sure where I'm going wrong but I've been trying to figure this out all day and I'm getting nowhere.
Any help that could be offered would be appreciated.
go:-
repeat,
f([],0,lon,spa,OP,OD),
write(OP),
write(OD),
fail.
city(lon).
city(ath).
city(spa).
city(kol).
path(lon,1,ath).
path(ath,3,spa).
path(spa,2,kol).
path(lon,1,kol).
joined(X,Y,D):-
path(X,D,Y);path(Y,D,X).
f(Ci_Vi,Di,De,De,PaO,Di):-
append([De],Ci_Vi,PaO),
!.
f(Cities_Visited,Distance,Start,Destination,Output_Path,Output_Distance):-
repeat,
city(X),
joined(Start,X,D),
not_member(X,Cities_Visited),
New_Distance is Distance + D,
f([Start|Cities_Visited],New_Distance,X,Destination,Output_Path,Output_Distance).
not_member(X,List):-
member(X,List),
!,
fail.
not_member(X,List).
The output I'm expecting here is [spa,ath,lon]4 [spa,kol,lon]3.
Once again, any help would be appreciated.
Many thanks in advance.
Your solution is essentially correct. Type f([],0,lon,spa,OP,OD), and you get the first path as expected. The only error I can see is that you're using repeat within your search predicate, which is why you keep computing the same solution. repeat is almost never necessary within business logic - backtracking for solutions is already built into the REP loop. Take it out, and you'll get the second path as expected, and then (correctly) failure.

Mac hash function broken

I'm more or less attempting to determine crypography algoirthms and how they work. I'm a little confused on proving how one is trivial.
For example:
MAC(xbit_key,Message) = xbit_hash(Message) XOR xbit_key
Take a look at this for a general explanation and that for a good example. If it's still not clear, come back with a more specific question.

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