Questions tagged [primitive-recursion]
66 questions
14
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What can be proven regarding the differences in power between unary ECMAScript regex functions and primitive recursive functions?
In 2014, inspired by Regex Golf, I started exploring, along with a mathematician going by the name teukon, what could be done in the unary domain in ECMAScript regex that went significantly beyond matching primes and powers of 2 (both of which were…
Deadcode
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7
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Primitive Recursion equipped with an evaluator function
The wikipedia article for primitive recursion mentions a limitation that primitive recursive function can't compute the function $ ev(i,j) $ which computes the $ i $th primitive recursive function on input $ j $.
I was wondering what you can compute…
cardobard_box
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7
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2 answers
primitive recursive functional equivalence
Given two primitive recursive functions is it decidable whether or not they are
the same function? For example lets take sorting algorithms A, and B which are
primitive recursive. While there are many algorithms for sorting they all
describe the…
44701
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6
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1 answer
How can the class of tail recursive functions be compared to the classes of PR and R?
How can the class of tail recursive functions (TR) be compared to the classes of primitive recursive functions (PR) and recursive functions (R)?
The computation of a PR function always halts. This does not apply to TR functions.
Given a tail…
Peter
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5
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The evolution of the term "recursive" from Goedel to Church to present day
I'm currently studying some of the history of computation / computability, in the early days known as recursion theory.
I see Goedel's definition of recursive functions seems significant in his paper, and Church uses his own definition of recursive…
Greg Peckory
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5
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1 answer
How can primitive recursion in two variables be made to be of only one variable?
Problem 7.16 in The Nature of Computation reads as follows:
[...] show that when defining primitive recursive functions, we really only need to think about functions of a single variable. In particular, show that a function $f(x)$ is primitive…
Sebastian Oberhoff
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5
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4 answers
Showing that the number of primitive-recursion programs for each function is countably-infinite
Problem Statement
Prove that if a function $f$ is primitive recursive, then there are countably infinite number of primitive recursive definitions of $f$
Yes, this is a homework question.
My Work
I proved that there are infinite number of…
Banach Tarski
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5
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2 answers
Decidability of dependent typing on primitive recursive languages
With a dependent type system in a normal functional language type checking may never halt. This is partially because dependent typing removes the isolation between types, and code. My question is this: would an implementation of dependent typing for…
44701
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5
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1 answer
Implementing primitive recursive functions in a programming language
I started studying Design Concepts in Programming Languages by Turbak, Gifford and Sheldon. In the first chapter, they define a language called POSTFIX, similar to a postfix calculator's input language. This one also has a conditional command and a…
meguli
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4
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Is there a name for the class of functions whose totality can be proved using "Ackermann-like" reasoning?
Primitive recursion is recursion where totality can be proved because there is a single natural number parameter that strictly decreases in every recursive call. Put another way, the recursion terminates because there is a parameter with order type…
Aaron Rotenberg
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4
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How to handle an undefined case with µ-recursive functions?
How to construct my proof and generally what should I aim to get when showing a function is $\mu$-recursive? Should I transform it in some of the basic functions using the given operators?
For example, how should I proceed with the following…
user8
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4
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1 answer
Primitive Recursion and course-of-values recursion - examples?
I ran into examples that I not trivially understand on course-of-values recursion,
In defining a function by primitive recursion, the value of the next
argument $f(n+1)$ depends only on the value of the current argument
$f(n)$. Definition of…
LogicLove
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3
votes
2 answers
Primitive recursive plus Ackermann
Let us consider the class $\cal F$ of functions that contains
all constant functions
all projections
the successor function
the Ackermann function
as basic functions, and that is closed under composition and primitive recursion.
(If we remove the…
Gamow
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3
votes
1 answer
what are Structural recursion, primitive recursion, recursion combinator and recursion principles?
Recently, I encountered terminologies such as primitive recursion and recursion combinator. One of the sources is here link
I googled and read some, but missing the points of them. I know that recursion occurs when a function appears within its…
alim
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3
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Total functional computable real numbers
Is there any computable real number which can not be computed by a higher order primitive recursive algorithm?
For computable real number I mean those that can be computed by a Turing machine to any desired precision in finite time. For higher order…
user3368561
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