Questions tagged [computer-science]

All mathematical questions about computer science, including theoretical computer science, formal methods, verification, and artificial intelligence. For questions about Turing computability, please use the (computability) tag instead. For numerical analysis, use the (numerical-methods) tag. For questions from scientific computing, use (computational-mathematics).

Computer science is the study of the theory, experimentation, and engineering that form the basics for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale.

Some fields of computer science such as computational complexity theory (which explores the fundamental properties of computational and intractable problems) are highly abstract, while fields such as computer graphics emphasize real-world visual applications.

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Computation with a memory wiped computer

Here is another result from Scott Aaronson's blog: If every second or so your computer’s memory were wiped completely clean, except for the input data; the clock; a static, unchanging program; and a counter that could only be set to 1, 2,…
Casebash
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How to Prove a Programming Language is Turing Complete?

I had some thoughts about how to prove the turing completeness of a programming language. I came to the conclusion, that if you could write a program that is able to parse a turing machine program, both should be equivalent as you could execute…
bot47
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Would Relational Calculus be Turing-Complete if it Allowed Unsafe Queries?

My understanding about Codd's concept of "safe queries" was created to ensure that a query would always terminate. One key ability of a Turing machine is that it can work on infinite calculations (and thus isn't guaranteed to terminate). If the…
Jason
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Is the $24$ game NP-complete?

The $24$ game is as follows. Four numbers are drawn; the player's objective is to make $24$ from the four numbers using the four basic arithmetic operations (in any order) and parentheses however one pleases. Consider the following generalization.…
Akhil Mathew
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What does it mean to say a language is context-free?

What does it mean to say a language is context-free?
user9377
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What math should a computer scientist take in college?

I'm a computer science major and like many of us we have to take two additional sciences. These two additional science courses are in addition to three semesters of calculus,two semesters of physics, and one semester each of linear algebra and…
lampShade
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What is a good language to develop in for simple, yet customizable math programs?

I'm writing to ask for some guidance on choosing a language and course of action in learning programming. I've seen thread after thread with questions from newbies, asking, "What is the best language to start with?" and then it always starts a flame…
drury
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Is there any mathematical operation on Integers that yields the same result as doing bitwise "AND"?

I'll provide a little bit of a background so you guys can better understand my question: Let's say I have two positive, non-zero Binary Numbers.(Which can, obviously, be mapped to integers) I will then proceed onto doing an "AND" operation for each…
Felipe
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What is the current status of Vinay Deolalikar's proof that P is not equal to NP

This could be mathematics or computer science, but also statistical physics, so I hope it qualifies for interest. I am aware that there were reservations about the proof $P \neq NP$, but no fatal flaws. I have followed Terence Tao's blog and Tim…
Gordon
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Are there any known barriers to some approach for solving P vs. NP?

Are there any known barriers to show the following invariant (perhaps by some sort of induction)? Let $\Sigma$ be some finite alphabet with $|\Sigma| \geq 2$, let $M$ be some (deciding) deterministic Turing machine with input alphabet $\Sigma$, and…
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An algorithm to convert float number to binary representation

I want to know the algorithm of converting a given float (e.g, 3.14) to binary in the memory. I read this wikipedia page, but it only mentions about the conversion the other way. Let me quickly give the details, from the same wikipedia page: As you…
Sait
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Is the set of non finitely describable real numbers closed under addition and squaring?

Is the set of non finitely describable real numbers closed under addition and squaring? If so, can someone give a proof? Thanks.
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Time complexity of binary multiplication?

Using the grade school method of multiplying two binary numbers takes $O(n^2)$ time, where $n$ is the length of the number in bits. Why is this true?
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Finite strings from infinite alphabet

Is the set of all strings of finite length $\Sigma^*$ from a infinite alphabet $\Sigma$ uncountable? The usual procedure in these types of proof is that you list strings of length 1 list strings of length 2 list strings of length…
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Tilde approximation for $\frac{N^{100}}{2^N}$?

I am having some trouble getting the tilde approximation for a computer algorithms class. Here is what I have so far: $\frac{N^{100}}{2^N} \rightarrow \lg\left(\frac{N^{100}}{2^N}\right) = \lg(N^{100}) - \lg(2^N) = 100\lg(N) - N\lg(2)$ From here I…
mrQWERTY
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