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EPAL, the language of even palindromes, is defined as the language generated by the following unambiguous context-free grammar: $S \rightarrow a a$ $S \rightarrow b b$ $S \rightarrow a S a$ $S \right …

Show that $L=\{a^{n^2} | n \geq 0\}$ is not regular Hey guys. I'm taking a CS class and this stuff is really new to me so bear with me. I tried to look if I get some contradiction by using the pumpi …

I was solving this equation: $$\text{key}=\left(\sum_{K=0}^n\frac{1}{a^K}\right)\bmod{m}.$$ Given $$ 1,000,000,000 < a, n, m \; < 5,000,000,000, $$ $$ a, m \text{ are coprime}. $$ I solved it by brute …

Is it possible to reduce MaxUNSAT to MaxSAT in a polynomial way ? When considering the MaxSAT problem, one often considers also the MinUNSAT problem, which is almost the same. And for a propositional …

I am trying to teach myself the principles of cryptograhpy, and want to solve the following question: Let G be the algorithm that takes an input x = (x1, . . . , xn) from {0, 1} n (so each xi ∈ {0, 1 …

Given an adjacency matrix $A_G$ of an undirected graph $G$, it is easy and straightforward to compute the characteristic polynomial $\chi_G(\lambda)$. What about the other way around? The problem can …

Let $f(N)$ be the average number of full nodes (nodes with two children) in an $N$-node binary search tree. Determine the values of $f(0)$ and $f(1)$. Given that for $N > 1$, $\qquad \displaystyle …

Doing the following exercise: Let $\overline{HALT(x,y)}$ be defined as $\overline {HALT(x,y)} \iff \text{program number y never halts on input x}$ Show that it is not computable. Just want to make s …

Subset-sum: Given a list of numbers, find if a non-empty sublist has sum 0 (there's a variation where we want sum=k instead of 0, but 0 is easier for analysis) Partition: Given a list, can it be part …

I was reading a few notes on Proof by Restriction and I am confused: A Valid Proof by Restriction is the following: Directed Hamiltonian Cycle Problem is NP Complete because if we look only at instanc …

I am a bit confused. Somehow I have a problem connecting two problems together. The Closest String problem and the problem of matching with mismatches. They seam to be related but, I fail to see the c …

I have the following homework problem: A 10 TB disk drive has an MTTF of 6,000,000 hours. How much data can we store in a system comprised of these disks, if we want the system MTTF to be at least 1 …

I'm doing an exercise from my book that says: Let $r$ and $s$ be arbitrary regular expressions over the alphabet $\Sigma$. Find a simpler equivalent regular expression: a. $r(r^*r + r^*) + r^*$ b. $( …

I have been given a question about a stack program which I can not solve. Write a stack program to evaluate the term $\qquad (((A+B)-(A*B))*C)/(((A-B-C))⁄2)$ How do I approach this problem?

I mean Dijkstra's algorithm for the shortest path. In all descriptions that I saw (including wikipedia), on every step, it always selects the nearest neighbor based on examining their weights. Imagine …