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 …
Category: Uncategorized
[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]: 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]: 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]: 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]: 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]: 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]: 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]: Creating a Self Ordering Binary Tree
Problem Detail: I have an assignment where I need to make use a binary search tree and alter it to self order itself such that items that are accessed the most (have a higher priority) are at the top of the Read More …
[Solved]: Complexity of multiplication
Problem Detail: I’ve been reading around the area of complexity and arithmetic operations using logic gates; one thing that is confusing me is that begin{equation} Theta (n^{2}) end{equation} is quoted as being the complexity for multiplication for iterative adition. But addition Read More …