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Practical importance of Turing machines?

I am an electrical engineer, and only had one CS course in college 26 years ago. However, I am also a devoted Mathematica user. I have the sense that Turing Machines are very important in computer science. Is the importance only in the theory of…
Ted Ersek
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How asymptotically bad is naive shuffling?

It's well-known that this 'naive' algorithm for shuffling an array by swapping each item with another randomly-chosen one doesn't work correctly: for (i=0..n-1) swap(A[i], A[random(n)]); Specifically, since at each of $n$ iterations, one of $n$…
Steven Stadnicki
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What threads share in general?

Well this is general question. And if anyone want to make it implementation specific then I will prefer Unix related stuff. But first need to know following problems in generality: I read single process can have multiple threads. Multiple threads of…
Mahesha999
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How does a computer determine the data type of a byte?

For example, if the computer has 10111100 stored on one particular byte of RAM, how does the computer know to interpret this byte as an integer, ASCII character, or something else? Is type data stored in an adjacent byte? (I don't think this would…
Bassinator
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Is there a more intuitive proof of the halting problem's undecidability than diagonalization?

I understand the proof of the undecidability of the halting problem (given for example in Papadimitriou's textbook), based on diagonalization. While the proof is convincing (I understand each step of it), it is not intuitive to me in the sense that…
user118967
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1 answer

Rice's theorem for non-semantic properties

Rice's theorem tell us that the only semantic properties of Turing Machines (i.e. the properties of the function computed by the machine) that we can decide are the two trivial properties (i.e. always true and always false). But there are other…
Kaveh
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33
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4 answers

How to show that a "reversed" regular language is regular

I'm stuck on the following question: "Regular languages are precisely those accepted by finite automata. Given this fact, show that if the language $L$ is accepted by some finite automaton, then $L^{R}$ is also accepted by some finite; $L^{R}$…
Cat
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What are system clock and CPU clock; and what are their functions?

While reading a book, I came across a paragraph given below: In order to synchronize all of a computer’s operations, a system clock—a small quartz crystal located on the motherboard—is used. The system clock sends out a signal on a regular basis…
swdeveloper
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3 answers

Pumping lemma for simple finite regular languages

Wikipedia has the following definition of the pumping lemma for regular langauges... Let $L$ be a regular language. Then there exists an integer $p$ ≥ 1 depending only on $L$ such that every string $w$ in $L$ of length at least $p$ ($p$ is…
Phil Wright
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3 answers

Encoding 1-out-of-n constraint for SAT solvers

I'm using a SAT solver to encode a problem, and as part of the SAT instance, I have boolean variables $x_1,x_2,\dots,x_n$ where it is intended that exactly one of these should be true and the rest should be false. (I've sometimes seen this …
D.W.
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Equivalence of Büchi automata and linear $\mu$-calculus

It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automaton. But, apparently, Büchi automata are a more powerful, expressive model. I've heard somewhere that Büchi automata are equivalent to linear-time $\mu$-calculus…
Daniil
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Will hardware/implementation affect the time/space complexity of algorithms?

I’m not even a CS student, so this might be a stupid question, but please bear with me... In the pre-computer era, we can only implement an array data structure with something like an array of drawers. Since one have to locate the drawer with…
nalzok
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How do Functional Reactive Programming and the Actor model relate to each other?

FRP is about streaming events and behaviours through pure functions. The Actor model - at least, as implemented in Akka - is about streaming immutable messages (which can be considered to be discrete events) through potentially impure objects,…
Robin Green
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What happens when an internet connection is faster than the storage write speed?

If one attempted to download a file at a speed of 800 Mb/s (100 MB/s) onto a hard drive with a write speed of 500 Mb/s (62.5 MB/s), what would happen? Would the system cap the download speed?
ymulki
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Can Quantum Computing solve Problems not even a Turing Machine can solve?

In his book "The Fabric of Reality", Penguin Books 1998, p. 218, David Deutsch says that the first quantum computer (built 1989 in the office of Charles Bennet, IBM Reasearch) "became the first machine ever to perform non-trivial computations that…
ggreiter
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