Problem Detail: I was reading an article that describes the switch between user-space and kernel-space that happens upon a system call. The article says An application expects the completion of the system call before resuming user-mode execution. Now, until now I Read More …
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Clear, intuitive derivation of the fixed-point combinator (Y combinator)?
Problem Detail: The fixed-point combinator FIX (aka the Y combinator) in the (untyped) lambda calculus ($lambda$) is defined as: FIX $triangleq lambda f.(lambda x. f~(lambda y. x~x~y))~(lambda x. f~(lambda y. x~x~y))$ I understand its purpose and I can trace the execution Read More …
Context-free grammar to a pushdown automaton
Problem Detail: I’m trying to convert a context free grammar to a pushdown automaton (PDA); I’m not sure how I’m gonna get an answer or show you my progress as it’s a diagram… Anyway this is the last problem I have Read More …
Is it really possible to prove lower bounds?
Problem Detail: Given any computational problem, is the task of finding lower bounds for such computation really possible? I suppose it boils down to how a single computational step is defined and what model we use for the proof, but given Read More …
What is the significance of context-sensitive (Type 1) languages?
Problem Detail: Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a state machine with no external memory (i.e., a finite automaton), Type 2 by a state machine with a single stack (i.e. a push-down automaton) and Read More …
What exactly is polynomial time?
Problem Detail: I’m trying to understand algorithm complexity, and a lot of algorithms are classified as polynomial. I couldn’t find an exact definition anywhere. I assume it is the complexity that is not exponential. Do linear/constant/quadratic complexities count as polynomial? An Read More …
Represent a real number without loss of precision
Problem Detail: Current floating point (ANSI C float, double) allow to represent an approximation of a real number. Is there any way to represent real numbers without errors? Here’s an idea I had, which is anything but perfect. For example, 1/3 Read More …
How can it be detected that a number generator is not really random?
Problem Detail: I heard that random number generation in computers isn’t really random, but there is no efficient algorithm to detect it. How can it be detected at all ? Asked By : URL87 Answered By : SamM Computers Being Really Random: True Read More …
How to analyze/test a binary search algorithm?
Problem Detail: I was asked to “Compute the average runtime for a binary search, ordered array, and the key is in the array.” I’m not quite sure how to approach this problem. Isn’t the runtime of binary search O(log n)? And Read More …
What are Markov chains?
Problem Detail: I’m currently reading some papers about Markov chain lumping and I’m failing to see the difference between a Markov chain and a plain directed weighted graph. For example in the article Optimal state-space lumping in Markov chains they provide Read More …
