Unanswered Questions
10,519 questions with no upvoted or accepted answers
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On unsatisfiable 2SAT formulas under some restriction
Let $\mathcal C(2,k)$ be set of satisfiable $2SAT$ formulas in $\leq k$ variables where for any two variables $x$ and $y$, out of the four clauses
a. $x\vee y$
b. $\neg x\vee y$
c. $x\vee\neg y$
d. $\...
- 2,937
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Self-referential text string compression
Can a text string contain a lossless compression of itself as a substring? I asked Gemini free, which wasn't sure but thought the answer is 'no', and ChatGPT free, which claimed it is 'no' except in ...
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How can I think about one statement that $TM_1$ uses $TM_2$ to compute $TM_3$?
In title, $TM_1$, $TM_2$ and $TM_3$ are all turing machines.
In book Computational Complexity: A Modern Approach by Sanjeev Arora et al, the proof of the non-computability of the HALTING problem is ...
- 2,999
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Knuth-Bendix completion as a context-sensitive grammar
I was wondering if the following is correct and looking for advice on how to develop it.
This was motivated by wondering how many distinct monoids of order 3 there exist up to isomorphism.
I ...
- 172
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How to transfer Hamilton cycle problem in non-directed graph to zero-one equation?
There are many discussions showing how to reduce Zero-One Equation problem to Hamilton cycle problem in a non-directed graph. However, none of these shows opposite transferring. I need to find a ...
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Two pseudo-perfect bipartite matchings
Given is a bipartite graph $G=(A,B;E)$ with $|B| = 2|A|$. Suppose we want to decide whether $B$ can be partitioned into two equal-size parts $B_1,B_2$ such that there is a perfect matching between $A$ ...
- 133
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Gödel sentences for Turing machines
Gödel's first incompleteness theorem states that any consistent, sufficiently expressive formal system of arithmetic on the natural numbers (one capable of performing both addition and multiplication) ...
- 209
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What algorithm can be used to implement code folding for the C programming language?
I'm working on a simple editor for the C programming language (without using an AST), and I need to implement a code folding feature.
When the user opens a file, an initial parse is performed, and all ...
- 121
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Seeing AM and MA in terms of "overwhelming majority" quantifier
The lecture notes here [1,2], mention the characterization of the complexity classes $AM$ and $MA$ in terms of quantfiers. More precisely, one can define a quantifier class $\exists\circ BP$ as
$L \...
- 2,999
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+50
Basic question about parallel repetition in IP protocol
The book Sanjeev Arora and Barak defines class IP (interactive protocol) by making the verifier have private coins. Before proceeding to public coin proofs and showing they are the "same," ...
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Has a Torus data structure been constructed?
It would be comprised of elements similar to a linked list. The elements would look something like:
...
- 111
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What is the complexity of checking whether a non-linear recursive datalog rule is one-bounded?
It is known that deciding whether a linear recursive datalog rule is one-bounded is NP-hard [1].
That is, given a rule such as: "p(x,y) :- q(x), p(y,z), r(z, ...) ,...", where the predicate ...
- 529
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Algorithm to compute a non-uniform rectangular grid on a domain based on a function defined on that domain
I have been trying to write a program to do the following:
I have a function on a domain, D. The function is very complicated, but it is essentially zero in a significant part of the domain. Now, I ...
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What is a better than check all $N!$ permutations of vertices way of canonicalizing a DAG of up to 100 nodes and bounded degree of <= 16?
The labels on my DAGs are things like $A\times B$ but encoded in Unicode chars. Nauty is a no-go for me, and it doesn't work on multi-digraphs unless you encode them using a number on a single edge.
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- 628
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Technique to prove/disprove if an Algorithm satisfies Deadlock Freedom or Mutual Exclusion
Regarding the following question:
Let A be an arbitrary correct deadlock-free mutual exclusion algorithm such that its exit code is not wait-free, the number of steps in the exit code of A depends on ...
