Problem Detail: I’m looking to work out the big-O notation for the following: $$frac{n^{s + 1} – 1}{n – 1} – 1$$ I have a feeling the result is $Oleft( n^s right)$ but I’m not sure how to prove it. Any Read More …
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[Solved]: How does an Operating System without kernel mode works?
Problem Detail: Andrew S. Tanenbaum in his book “Modern Operating Systems 3rd Edition” states that the distinction between operating system software and normal (user mode) software can sometimes be blurred in embedded systems(which may not have kernel mode) Can someone please Read More …
[Solved]: Which priority queue implementations are stable?
Problem Detail: I can’t answer this question. It seems simple but I really don’t know how to approach it. Here it is: A priority queue is said to be stable if deletions of items with equal priority value occur in the Read More …
[Solved]: About Control Unit in CPU and Clock Cycle
Problem Detail: I’ve been studying about CPU and I am trying to implement a small CPU, like MU0. Control unit gets instruction and generates and gives several control signals to other parts of CPU, such as ALU, PC, ACC, etc. And Read More …
[Solved]: Finite State Machine that only accepts strings with equal number of 0’s and 1’s
Problem Detail: Question: Suppose you have a finite state machine that accepts only strings with an equal number of zeros and ones. Show that you can then construct a finite state machine that accepts only strings of the form 0^n 1^n, Read More …
[Solved]: Defining a context-free grammar for ${w in {0, 1}^* : #_0(w) = #_1(w)}$
Problem Detail: I have a language where each string in the language has even amount of $0$’s as $1$’s (e.g., $0101$, $1010$, $1100$, $0011$, $10$ are all in the language). I was hoping to define a context-free grammar that describes this Read More …
[Solved]: Ant colony optimization for continuous functions
Problem Detail: I am trying to do optimization of a voice activity detection function, which is a function with continuous parameters. This is easily accomplished with genetic algorithms, simulated annealing, and tabu search, but I’m somewhat confused on how to accomplish Read More …
[Solved]: Using pumping lemma to show $L = {a^i b^j a^k | k > i + j}$ cannot be accepted by an FA
Problem Detail: $L = {a^i b^j a^k | k > i + j}$ Use the pumping lemma to show that this language cannot be accepted by an FA. Proof: Suppose $L$ can be accepted by an FA. Suppose a string Read More …
[Solved]: In the Miller-Rabin primality test, for a composite number, why are at least $frac{3}{4}$ of the bases witnesses of compositeness?
Problem Detail: The following is an excerpt from the Wikipedia article on the Miller-Rabin primality test: It can be shown that for any odd composite $n$, at least $frac{3}{4}$ of the bases $a$ are witnesses for the compositeness of $n$. In Read More …
[Solved]: Types of Automated Theorem Provers
Problem Detail: I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. Which are the relevant automated theorem provers? I found A Review of Theorem Provers Read More …
