Problem Detail: I’m trying to make a turing machine that will take in a binary string as input x and output the binary representation of the length of x. So M(0110) returns 100, M(1010101010) returns 1010, ect. It also has to Read More …
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[Solved]: Is $epsilon$ always contained in $Sigma^*$?
Problem Detail: Please correct me on any terminology. For some reason I’m a bit confused. $Sigma = {epsilon, 0, 1}$ This means my alphabet, $Sigma$, contains three symbols ($epsilon, 0, 1$). $Sigma^*$ is the language over $Sigma$, and it equals ${epsilon, Read More …
[Solved]: Convert RE to DFA
Problem Detail: I’ve been trying to convert a regular expression to a non-deterministic finite automata (NFA) first using Thompson’s construction, giving: , which looks correct. I am then using subset construction to create the DFA from the NFA, shown here. But Read More …
[Solved]: What are the k characters which make the most complete words?
Problem Detail: Given a word list of $N$ words formed from a language of $M$ characters, where each word is composed of $n geq 1$ not necessarily distinct characters, how can I find the best set of $k<M$ characters to learn, Read More …
[Solved]: Are there any specific problems known to be undecidable for reasons other than diagonalization, self-reference, or reducibility?
Problem Detail: Every undecidable problem that I know of falls into one of the following categories: Problems that are undecidable because of diagonalization (indirect self-reference). These problems, like the halting problem, are undecidable because you could use a purported decider for Read More …
[Solved]: Concatenation of the intersection of two languages
Problem Detail: I’m enrolled to a Formal Language And Automata course, and we have to prove this equation on sets of strings: $$(L_1cap L_2)cdot L_3 ≠ (L_1cdot L_3) cap (L_2cdot L_3)$$ I’ve tried a lot of sets for e.g. $L1 = Read More …
[Solved]: How close are common programming languages to not being Turing complete?
Problem Detail: The term “Turing completeness” has been discussed in several of the Computer Science classes that I’ve taken. However, I’ve never gotten an intuitive feel for what Turing completeness actually requires. I found this question, but the answers are a Read More …
[Solved]: Solving recurrence relation with two recursive calls
Problem Detail: I’m studying the worst case runtime of quicksort under the condition that it will never do a very unbalanced partition for varying definitions of very. In order to do this I ask myself the question what the runtime $T(n, Read More …
[Solved]: How many states when converting CFG to PDA
Problem Detail: When converting a CFG to a PDA I know that you get three main states, Qstart, Qloop and Qaccept. But Qloops will need a various amount of states, and my question is how many? Is there a way to Read More …
[Solved]: Viterbi algorithm recursive justification
Problem Detail: I have a question regarding recursion in Viterbi algorithm. Define $pi(k; u; v)$ which is the maximum probability for any sequence of length $k$, ending in the tag bigram $(u; v)$. The base case if obvious $pi(0,*,*)=1$ The general Read More …
