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Is there an equation $f(k,m,n)=n$ where $n$ is the number of applications of the Ackermann function needed?
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Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$
Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?
Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.
Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.
recursion tetration hyperoperation ackermann-function
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
asked Jul 15 at 4:05
user189728
33329
 |Â
show 4 more comments
up vote
0
down vote
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Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$
Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?
Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.
Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.
recursion tetration hyperoperation ackermann-function
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
asked Jul 15 at 4:05
user189728
33329
Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
1
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
 |Â
show 4 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$
Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?
Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.
Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.
recursion tetration hyperoperation ackermann-function
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
asked Jul 15 at 4:05
user189728
33329
Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$
Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?
Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.
Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.
recursion tetration hyperoperation ackermann-function
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
asked Jul 15 at 4:05
user189728
33329
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
edited Aug 10 at 12:50
Simply Beautiful Art
49.4k572172
49.4k572172
asked Jul 15 at 4:05
user189728
33329
asked Jul 15 at 4:05
user189728
33329
asked Jul 15 at 4:05
user189728
33329
33329
Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
1
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
 |Â
show 4 more comments
Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
1
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
1
1
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
 |Â
show 4 more comments
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Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40
1
@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55
Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58
@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59
Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59