Author: ignougroup

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Problem Detail: I’m wondering if there is a good example for an easy to understand NP-Hard problem that is not NP-Complete and not undecidable? For example, the halting problem is NP-Hard, not NP-Complete, but is undecidable. I believe that this means Read More …

Problem Detail: OK, so here is a question from a past test in my Theory of Computation class: A useless state in a TM is one that is never entered on any input string. Let $$mathrm{USELESS}_{mathrm{TM}} = {langle M, q rangle Read More …