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1500 questions
11
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2 answers
Chromatic polynomial of a square
Consider a square, ABCD. Intuitively it seemed to me that its chromatic polynomial is $\lambda(\lambda - 1)(\lambda - 1)(\lambda - 2)$ where there are $\lambda$ colours available..
That is there are $\lambda$ ways in which a colour for A can be…
Abhijith Madhav
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1 answer
If $\mathbf{P} = \mathbf{NP}$, then is $\mathbf{L} = \mathbf{NL}$?
If $\mathbf{P} = \mathbf{NP}$, then is $\mathbf{L} = \mathbf{NL}$? I am asking this question because, for other non-deterministic classes, it seems $\mathbf{P} = \mathbf{NP}$ always establishes that they are equal to their deterministic…
ttr
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11
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5 answers
How is the key in a private key encryption protocol exchanged?
Windows NT used a point-to-point protocol where a client can communicate "securely" with a server by using a stream cipher to encrypt an array of messages with some key $k$. The server also encrypts its response with the same key $k$. But how is it…
codd
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11
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4 answers
Why is the tape not part of the definition of a Turing Machine?
I've wondered why the tape/tapes are not part of the formal definition of a Turing Machine. Consider, for example, the formal definition of a Turing machine on Wikipedia page. The definition, following Hopcroft and Ullman, includes: the finite set…
Shuzheng
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11
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7 answers
List of intro TCS books for those who don't know much about TCS
If you have to recommend books for someone who wants to learn more about TCS at the introductory level such as automata theory, algorithmics, complexity theory, etc, what book(s) would you recommend for those who are interested and want to learn…
Ken Li
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11
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1 answer
What is the relationship between problems and languages?
I want to ask exactly what is the relationship between problems and languages.
We know that the set of all languages uncountable.
Is the set of problems also uncountable?
Can every problem be defined by a language?
Can a language solve more than…
Ravi Singh
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11
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1 answer
How do you determine the number of errors in the Welch-Berlekamp algorithm?
In the Welch-Berlekamp algorithm for decoding Reed-Solomon codes, one is given a list of points $(a_i, b_i)$ representing a message with $e$ errors on the $b_i$ in unknown locations (and $e$ is given to the algorithm). The output is a polynomial…
JeremyKun
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11
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2 answers
Is HORN-SAT in LIN, if so why is that not an indication that P=LIN?
The Complexity Zoo defines $LIN$ to be the class of decision problems solvable by a deterministic Turing machine in linear time.
$$LIN \subseteq P$$
Since HORN-SAT is solvable in $O(n)$ (as indicated in Linear-time algorithms for testing the…
Archy Will He 何魏奇
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11
votes
3 answers
Data General MV/8000 virtues of "No mode bit"
I'm reading Tracy Kidder's "The Soul of a New Machine" where a team at Data General design a new machine (codenamed "Eagle", later named MV/8000). It is 32-bit extension of a previous architecture (the 16-bit Eclipse). One of the revolving themes…
Morty
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11
votes
2 answers
Good mathematical book on algorithms
I’m a sucker for mathematical elegance and rigour, and now am looking for such literature on algorithms and algorithm analysis. Now, it doesn’t matter much to me what algorithms are covered, but very much how they are presented and treated.¹ I most…
k.stm
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11
votes
3 answers
How do I tell if a comparison network sorts?
I am presented with a comparison network. How can I determine if the comparison network is a sorting network? In the image below there is an example of a selection sort and insertion sort network. The intent is to have a comparison network and sort…
gogasca
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11
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2 answers
CCS process for a drink dispenser with two different prices
A drink dispenser requires the user to insert a coin ($\bar c$), then press one of three buttons: $\bar d_{\text{tea}}$ requests a cup of tea $e_{\text{tea}}$, ditto for coffee, and $\bar r$ requests a refund (i.e. the machine gives back the coin:…
Gilles 'SO- stop being evil'
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11
votes
3 answers
Algorithms for minimizing Moore automata
Brzozowski's algorithm can be extended to Moore automata but its time complexity is exponential in general. Is there any other algorithm for minimization of Moore automata? What are the running times of these algorithms if any?
Ajeet Singh
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11
votes
3 answers
Why would you use a monitor instead of a semaphore?
I am currently attending the concurrent programming course in my university and we recently started talking about the concept of a monitor. While I understand the necessity of mutual exclusion, I do not understand why I would use a monitor for that.…
Dennis Hein
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11
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1 answer
How fast can we compute the size of maximum matching in an unweighted bipartite graph?
Is there a way to compute the size of a maximum matching
in an unweighted bipartite graph
more efficiently (e.g. faster) than computing a maximum matching?
It is a long shot but
it is often an interesting problem to avoid throwaway computations…
Yann
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