Problem Detail: According to wikipedia, every finite set is computable. Definition: set $S subset N$ is computable if there exists an algorithm which defines in finite time if a given number $n$ is in Set. Question: what is wrong with this Read More …
Author: ignougroup
[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 …
[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]: 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 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]: Is SAT in P if there are exponentially many clauses in the number of variables?
Problem Detail: I define a long CNF to contain at least $2^frac{n}{2}$ clauses, where $n$ is the number of its variables. Let $text{Long-SAT}={phi: phi$ is a satisfiable long CNF formula$}$. I’d like to know why $text{Long-SAT} in P$. First I thought Read More …
[Solved]: Shifting subset sum solution by constant positive integer
Problem Detail: While reading the Wikipedia article about the subset sum problem I came across this example: “is there a non-empty subset whose sum is zero? For example, given the set ${ −7, −3, −2, 5, 8 }$, the answer is Read More …
[Solved]: Example for a non-trivial PCP verifier for an NP-complete problem
Problem Detail: During my involvement in a course on dealing with NP-hard problems I have encountered the PCP theorem, stating $qquaddisplaystyle mathsf{NP} = mathsf{PCP}(log n, 1)$. I understand the technical definition of a PCP verifier, so I know in principle what Read More …
[Solved]: Relation between space and time complexity for machines with write once read many (WORM) memory
Problem Detail: While thinking about different calculi for predicate logic (like natural deduction and sequent calculus), I noticed that these calculi are (often) presented in a form suitable for “human computers”. A “human computer” is limited to use write once read Read More …
[Solved]: Compression functions are only practical because “The bit strings which occur in practice are far from random”?
Problem Detail: I would have made a comment, as this pertains to Andrej Bauer’s answer in this thread; however, I believe it is worth a question. Andrej explains that given the set of all bit strings of length 3 or less, Read More …
