Problem Detail: In my Computer Logic class we were assigned the following problem: Complete a truth table that has $3$ inputs $(A, B,C)$ and one output $(F)$. $F$ is asserted whenever $B$ or $C$ are asserted, but deasserted if both $B$ Read More …
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[Solved]: Complexity of taking mod
Problem Detail: This seems like a question that should have an easy answer, but I don’t have a definitive one: If I have two $n$ bit numbers $a, p$, what is the complexity of computing $abmod p$ ? Merely dividing $a$ Read More …
[Solved]: Proving the set of finite languages is countable without using the union of countable sets
Problem Detail: The list of finite languages over a finite alphabet is countable. I could prove it by saying that the list of languages of size 1 is countable, the language of size 2 is countable, and so on. Then I Read More …
[Solved]: Regular expression for ${a^k b^m c^n mid k+m+n text{ is odd} }$
Problem Detail: I have to make a regular expression from the following laguage: {$a^kb^mc^n : $ where k + m + n is odd} Is is possible for the sum of three numbers to be odd (other than three consecutive odd Read More …
[Solved]: Find similar vector by Locality Sensitive Hashing
Problem Detail: I have many vectors in my database. They are in high dimensions such as: $v_1$ : $langle 23, 23, 1, 33, 103, 219, dots rangle$ $v_2$ : $langle 92, 83, 1, 33, 239, 192, dots rangle$ … I will Read More …
[Solved]: Rational agent question from Russell and Norvig
Problem Detail: Question from Artificial Intelligenge: A Modern Approach by Russell and Norvig (Exercise 2.1). Suppose that the performance measure is concerned with just the first $T$ time steps of the environment and ignores everything thereafter. Show that a rational agent’s Read More …
[Solved]: Multisets of a given set
Problem Detail: A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it counting repetitions. (a) What is the number of multisets of size Read More …
[Solved]: DFA drawing for binary string with substrings of minimum length 3 with at least two zeroes in each substring
Problem Detail: In trying to gain a better understanding of finite state machines, I stumbled across this idea and have been confused as to how to approach this case in terms of a DFA. The set of binary strings of length Read More …
[Solved]: Showing that deciding whether a given TM accepts a word of length 5 is undecidable
Problem Detail: I’m having trouble grasping this the concept of reductions. I found the solution and it looks like this: Assume that $M_5$ is a Turing Machine that can decide if a given Turing Machine $M$ accepts any string of length Read More …
[Solved]: Understanding the definition of SPMD
Problem Detail: From Wikipedia SPMD (single program, multiple data) is a technique employed to achieve parallelism; it is a subcategory of MIMD. Tasks are split up and run simultaneously on multiple processors with different input in order to obtain results faster. Read More …
