Problem Detail: I wonder whether the following language is a context free language: $$A = {w in {a,b,c}^* mid #_a(w) + 2#_b(w) = 3#c(w)}$$ where $#_x(w)$ is the number of occurrences of $x$ in $w$. I can’t find any word that Read More …
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[Solved]: Perfectly Secure Ciphers known other than the OTP
Problem Detail: By Information-Theoretic definitions, the One Time Pad (OTP) is called/was proved to be a Perfectly Secure Cipher. For the sake of completeness, we define OTP: An enc/dec function, $f:mathcal{P} times mathcal{K} rightarrow mathcal{C}$ Perfect Security: Given $m, m^* in Read More …
[Solved]: What is the difference between these terms?
Problem Detail: Between my textbook and various online sources (namely wikipedia), I’m very confused… can somebody clear up which words are synonymous and which mean different things? Many-to-one reduction Mapping reduction Turing reduction Cook reduction Karp reduction Polynomial-time many-to-one reduction Polynomial Read More …
[Solved]: the height of a tree given n nodes and a condition
Problem Detail: I came across a question on which I got totally stuck 🙁 a sort of homework question) A weight-balanced tree is a binary tree in which for each node. The number of nodes in the left sub tree is Read More …
[Solved]: Must a complete subgraph be induced?
Problem Detail: If we had some $K_n$ subgraph where $K_n subseteq G$, must the complete subgraph $K_n$ be an induced subgraph from $G$? In other words, can we create a situation where we remove vertices from a simple graph $G$ to Read More …
[Solved]: Modelling a basic sequential circuit as a transition system?
Problem Detail: I’m going through Dr Joost-Pieter Katoen’s slides and stumbled upon this: For some reason I can’t quite make out how the transition system relates to the sequential circuit. If I had a question for instance that asked me to Read More …
[Solved]: Why is this argument for $Pneq NP$ wrong?
Problem Detail: I know its silly, but i managed to confuse myself and i need help settling this Suppose $P=NP$, then clearly for every oracle $A$ we have $P^A=NP^A$ which contradicts the fact that there exists some oracle $A$ for which Read More …
[Solved]: More than one NFA accepting a given language
Problem Detail: While going through certain problems. it seems that more than one NFA is possible for the given language. Is it so? For example for drawing: NFA ending with 1 where $Sigma={0,1}$ is and also we can draw one without Read More …
[Solved]: Probability of Success in Slotted Medium Access
Problem Detail: Suppose you have a network which uses time division multiplexing (i.e. Slotted Aloha). There are $N$ nodes each transmitting in a given slot with probability $p$. I understand that the probability a node is successful in a slot is Read More …
[Solved]: How a reduction can help up solve a problem?
Problem Detail: I am studying the basics of Computation Theory and I came up with an example I can’t understand. Let’s have a language $L = {langle Mrangle mid L(M) = Sigma^{ast} }$, so $L$ contains codes of all Turing machines Read More …
