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 …
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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 …
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 …
Are all system calls blocking?
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 …
Why polynomial time is called “efficient”?
Problem Detail: Why in computer science any complexity which is at most polynomial is considered efficient? For any practical application(a), algorithms with complexity $n^{log n}$ are way faster than algorithms that run in time, say, $n^{80}$, but the first is considered Read More …
Can there be a perfect chess algorithm?
Problem Detail: Current chess algorithms go about 1 or maybe 2 levels down a tree of possible paths depending on the player’s move’s and the opponent’s moves. Let’s say that we have the computing power to develop an algorithm that predicts Read More …
Reduction from Vertex Cover to an Independent Set problem
Problem Detail: Assume there exists some algorithm that solves vertex cover problem in time polynomial in terms of $n$ and exponential for $k$ with the run time that looks like this $O(k^2 55^k n^3)$. Can we claim that independent set can Read More …
Is it decidable whether a TM reaches some position on the tape?
Problem Detail: I have these questions from an old exam I’m trying to solve. For each problem, the input is an encoding of some Turing machine $M$. For an integer $c>1$, and the following three problems: Is it true that for Read More …
SSTF disk scheduling algorithm? What if lowest seek times are equal in either direction?
Problem Detail: Using the Shortest-Seek-Time-First (SSTF) disk scheduling algorithm (where we select a request with a minimum seek time from the current head position), what happens if the requests in both directions from the current head position are equal? For example, Read More …
How to reduce the number of crossing edges in a diagram?
Problem Detail: I am working on a diagram editor. Diagrams display 2D shapes (nodes) connected with connectors (edges). I’d like to add an operation that, given a selection of nodes, “disentangles” them: it repositions them to reduce the number of crossing Read More …
