L in P/Poly but L not in P - complexity-theory

Show that there is a squatting language L:
L in P/Poly but L not in P
I'd like to read your explanations

Related

What are the inorder and postorder traversals of the following tree?

With respect to the following tree:
What is the correct inorder traversal?
U S T X C P Y R B A I G J F N H V T E D L
U S T X C P Y R B A D E I G J F N H V T L
What is the correct postorder traversal?
U T S X P R Y C B D I J G N V T H F E L A
U T S X P R Y C B I J G N V T H F E D L A
I evaluated both pairs. But some are saying 1-1 and 2-1 are correct, while others say 1-2 and 2-2 are correct. I'm confused. Which ones are actually correct?
inorder:
B U S T X C P Y R A D E I G J F N H V T L
postorder (2.2 is correct):
U T S X P R Y C B I J G N V T H F E D L A

How sorting list of string by length

Hi i having a problem with sort list like:
sort([p v q v r, p, p v q], R).
expected result is
R = [p, p v q, p v q v r]
Is any built in sort in swi-prolog which allow me that or i have to write it myself.

Passing return value into another method

I am starting with an array of letters:
letters = %w[c s t p b l f g d m
y o u i h t r a e l
o t l a e m r s n i
m a y l p x s e k d]
Passing them, finding all combinations that return an array like this ["cstp", "cstb", "cstl"], this is a shortened example.
def combinations(letters)
combos = letters.combination(4)
combos.collect do |letter_set|
letter_set.join(",").gsub("," ,"")
end
end
I am trying to figure out how to pass the return value of combinations into start_wtih_letter_c. Do I have to pass a block like &block? I tried various things that keep saying wrong number of arguments.
def start_with_letter_c(pass the return value)
combinations.select {|word| word.match(/^ca/) }
end
Here you go, no errors:
letters = %w[c s t p b l f g d m
y o u i h t r a e l
o t l a e m r s n i
m a y l p x s e k d]
def combinations(letters)
combos = letters.combination(4)
combos.collect do |letter_set|
letter_set.join(",").gsub("," ,"")
end
end
def start_with_letter_c(combinations)
combinations.select {|word| word.match(/^ca/) }
end
start_with_letter_c(combinations(letters))
# => ["cael", "caeo", "caet", "cael", "ca ...and so on
I would write something like this:
letters = %w[c s t p b l f g d m
y o u i h t r a e l
o t l a e m r s n i
m a y l p x s e k d]
def combinations(letters)
letters.combination(4).map(&:join)
end
def start_with_letter_c(combinations)
combinations.select { |word| word.start_with?('ca') }
end
start_with_letter_c(combinations(letters))

Element to search in binary tree in Prolog

I'm very new to Prolog, and trying to find an element to search in binary tree, it finds it successfully but the problem is if it doesn't it still gives yes, I want it to say no or to say not found. My code is:
child(1,2,3).
child(2,4,5).
child(3,6,7).
node(1,a).
node(2,b).
node(3,c).
node(4,d).
node(5,f).
node(6,f).
node(7,g).
show(X):-
write('element is found in node: '),write(X),nl.
inc(X,Y,Z):-
Y is X+X,
Z is X+X+1.
find(A):-
traverse3(1,A).
traverse3(X,A):-
check(X,A),
inc(X,Y,Z),
child(X,Y,Z),
traverse3(Y,A),
traverse3(Z,A).
check(X,A):- not(node(X,A)).
check(X,A):-
node(X,A),
show(X).
traverse3(X,A):- not(child(X,Y,Z)).
This is an unusual binary tree. But anyway, since you have already "normalized" it to a database representation, all you have to do to find an element is to ask for it.
In other words, if your program tree.pl consists only of the child/3 and node/2 facts:
child(1,2,3).
child(2,4,5).
child(3,6,7).
node(1,a).
node(2,b).
node(3,c).
node(4,d).
node(5,f).
node(6,f).
node(7,g).
You can simply query for the element you need:
?- [tree].
true.
?- node(N, a).
N = 1.
?- node(N, f).
N = 5 ;
N = 6.
?- node(4, E).
E = d.
?- node(N, E).
N = 1, E = a ;
N = 2, E = b ;
N = 3, E = c ;
N = 4, E = d ;
N = 5, E = f ;
N = 6, E = f ;
N = 7, E = g.
Or is there something I am missing?

Prolog - dyck path from origin to (2N,0)

Is called Dyck Path.
It is a plane of x and y axis,
where each step will be only (x+1,y+1) or (x+1,y-1)
and will always stay above x-axis
K should means the peak of the Dyck path.
When K is 2 it should means that the peak is 2 and 3.
to form a legal sequence list of matching the parentheses a = '(', and b = ')' and has length 2N
Eg. [a,a,b,b] and [a,b,a,b] are the legal list for N = 2
[a,b,b,a] and [b,a,b,a] do not satisfies for N = 2
need to define the predicate
listFind(L,K,N) satisfies when L has list of order of 2N, for some k >= K
For example
|?- listFind(L,1,3).
L = [a,b,a,b,a,b] ? ;
L = [a,b,a,a,b,b] ? ;
L = [a,a,b,b,a,b] ? ;
L = [a,a,b,a,b,b] ? ;
L = [a,a,a,b,b,b] ? ;
no
|?- listFind(L,2,3).
L = [a,a,b,b,a,b] ? ;
L = [a,a,b,a,b,b] ? ;
L = [a,a,a,b,b,b] ? ;
no
Thanks in advance.
the role of K is unclear to me. Anyway, here is a snippet satisying your test case:
listFind(L, K, N) :-
N2 is N*2,
length(L, N2),
phrase(dyck, L),
% satisfy condition on K
run_length_encoded(L, RLE),
[X-a|_] = RLE, X >= K.
% DCG for Dyck' language over alphabet `a,b`
dyck --> [] ; [a], dyck, [b], dyck.
run_length_encoded([X|S], C) :-
run_length_encoded(S, X, 1, C).
run_length_encoded([Y|S], X, N, E) :-
( X == Y
-> M is N + 1,
run_length_encoded(S, X, M, E)
; E = [N-X|T],
run_length_encoded(S, Y, 1, T)
).
run_length_encoded([], X, C, [C-X]).
As you can see, the interpretation of K is
the sequence must start with at least K consecutives a

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