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1500 questions
11
votes
2 answers
Is there a paradigm for composing "incremental update" functions in a pure dataflow style?
I don't know the correct terminology for asking this question, so I'll describe it with lots of words instead, bear with me.
Background, just so we're on the same page: Programs often contain caches - a time/memory tradeoff. A common programmer's…
Hallting
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11
votes
3 answers
Do "inductively" and "recursively" have very similar meanings?
Do "inductively" and "recursively" mean very similar?
For example, if there is an algorithm that determines a n-dim vector by determine its first k+1 components based on its first k components having been determined, and is initialized with the…
Tim
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11
votes
1 answer
Collection of APX-hard problems
Everyone knows "Garey & Johnson", which is my go-to reference whenever I need a problem to transform from for an NP-hardness proof. However I recently find myself in need of an APX-hardness proof, and I wonder if there is a similar (and more up to…
Lukas Barth
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11
votes
2 answers
How can I prove this language is not context-free?
I have the following language
$\qquad \{0^i 1^j 2^k \mid 0 \leq i \leq j \leq k\}$
I am trying to determine which Chomsky language class it fits into. I can see how it could be made using a context-sensitive grammar so I know it is atleast…
justausr
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11
votes
3 answers
Decidability of a problem concerning polynomials
I have come across the following interesting problem: let $p,q$ be polynomials over the field of real numbers, and let us suppose that their coefficients are all integer (that is, there is a finite exact representation of these polynomials). If…
042
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11
votes
3 answers
A d-ary heap problem from CLRS
I got confused while solving the following problem (questions 1–3).
Question
A d-ary heap is like a binary heap, but(with one possible exception) non-leaf nodes have d children instead of 2 children.
How would you represent a d-ary heap in an…
lucasKo
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11
votes
1 answer
When used as call stack, do garbage-free spaghetti stacks form a DAG?
I'm looking into implementation techniques for programming
languages, and recently came across spaghetti stacks, which are
supposedly a good fit for a continuation passing style model
(given their use in e.g.
Scheme and SML/NJ).
For sake of…
Rhymoid
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11
votes
3 answers
Why are regular expressions defined with union, concatenation and star operations?
A regular expresssion is defined recursively as
$a$ for some $a \in \Sigma$ is a regular expression,
$\varepsilon$ is a regular expression,
$\emptyset$ is a regular expression,
$(R_1 \cup R_2)$ where $R_1$ and $R_2$ are regular expressions is a…
Ali Shakiba
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11
votes
0 answers
When can you "invert" an equation in the lambda calculus
Suppose that $M$ is a full model of the simply typed lambda calculus. Suppose each base type is infinite.
Now suppose that $f$ and $g$ are two functions in $M$ (not necessarily in the same domain) that are not definable by any pure term, and that…
Andrew Bacon
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11
votes
0 answers
Denotational semantics of object-oriented languages
I am interested in denotational semantics of object oriented languages. Namely, what are the common/typical denotations of objects used in the literature? Is this an interesting topic these days?
The most comprehensive article I've found dates back…
zpavlinovic
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11
votes
3 answers
What are the applications of Rose trees?
I recently found out about the Rose tree data structure, but just going off of a Haskell data definition and the tiny Wikipedia description of it, I've got some trouble understanding what applications a Rose tree might have.
For reference, the…
Jules
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11
votes
1 answer
How did 'Isabelle' (the theorem prover) get its name?
The title says it all, but I'm curious because it isn't obvious how a theorem prover came to be named 'Isabelle'. Was it named for a person? I couldn't find out by some Google searches.
IIM
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11
votes
3 answers
How Do Common Pathfinding Algorithms Compare To Human Process
This might border on computational cognitive science, but I am curious as to how the process followed by common pathfinding algorithms (such as A*) compares to the process humans use in different pathfinding situations (given the same information).…
DorkRawk
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11
votes
1 answer
Indexing into a pattern database - Korf's Optimal Rubik's Cube solution
As a fun project, I've been working on a C# implementation of Richard Korf's - Finding Optimal Solutions to Rubik's Cube Using Pattern Databases.
https://www.cs.princeton.edu/courses/archive/fall06/cos402/papers/korfrubik.pdf
I actually have it…
Cosmosis
- 113
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11
votes
3 answers
Notions of efficient computation
A polynomial-time Turing machine algorithm is considered efficient if its run-time, in the worst-case, is bounded by a polynomial function in the input size. I'm aware of the strong Church-Turing thesis:
Any reasonable model of computation can be…
Mohammad Al-Turkistany
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