# sets's questions - English 1answer

242 sets questions.

### Prove/disprove that the class of decidable (resp. partially decidable) languages is closed under symmetric difference

Prove/disprove that the class of decidable (resp. partially decidable) languages is closed under symmetric difference. A symmetric difference of sets A and B is the set (A \ B) ∪ (B \ A). I know that ...

### Is it possible to add every word in a file to a set in $\mathrm{O}(n)$ time?

The Problem: I am currently analyzing a simple program that takes a file of length $n$, splits it into its individual words (seperated by white space) and adds those words to a set: ...

### Does the reduction of a language to another with a bijective function imply that they are equally solvable?

0 answers, 25 views reductions sets
I understand that if $A \leq B$ and $A$ is not a recursively enumerable set then $B$ is also not a recursively enumerable set. (and if $A \leq B$ and $B$ is decidable then $A$ is decidable) What if ...

### 1 Algorithm for Minimum Subset Needed to Satisfy all Constraints

I was wondering what is the most efficient algorithm to solve something like the following: You have $P$ people. You have $T$ tasks, each of which is a set of sets that represent all of the possible ...

### Backtracking solution to Bin Packing problem

0 answers, 32 views algorithms sets backtracking
I have the following problem : Given an Array of integers such as : V = {9,4,1,2,4,3} and a number such as N = 12 divide into K parts, so each part adds N or less, taking the best solution. I ...

### 3 Algorithm for minimum number of partitions to transform list of sets into Laminar Set Family

0 answers, 253 views algorithms graphs sets

### Is this problem NP-complete?

Let there be a set of cardinality $n\in \mathbb{N}$. Let there also be $n$ subsets of that set. What is the smallest k such that union of some $n-k$ of those subsets is of cardinality at most $k$? The ...

### 2 Given N sets of disjoint subsets, find a set of disjoint subsets such that it satisfies a criteria

1 answers, 90 views combinatorics sets set-cover partitions
Given a collection of sets $S_i$ of disjoint subsets $sub_i$ of a set $X$, find a set $A$ of disjoint subsets $asub$ such that each one of these subsets is subset or equal to at most one subset in ...

### 2 What is the algorithm for a decider to get the language accepted by a DFA?

I am trying to understand the larger problem of the decidability of the equality of two DFAs. I understand that this problem can be solved using minimizing DFAs, but my textbook states this can be ...

### 1 How to find sets of polynomially bounded numbers whose subset sums are different?

Let $n$ be any positibe integer and set $N=\{1,\dots,n\}$. Now select two arbitrary but different subsets of $N$, say $S$ and $S'$. We are interested in finding a function $\pi(A)=\sum_{i\in A}a_i$ ...

### 2 Prove: Every decidable set is Turing reducible to the empty set

2 answers, 172 views turing-machines reductions sets
Question- Prove: Every decidable set is Turing reducible to the empty set. Can anyone help me with this please? All reductions tutorials I've seen use practical examples of reduction such as sipser'...

### 3 Compact mapping from an involuted set

Let $S$ be a set (say positive integers $\leq$ N) and $f$ an involution ($f$ is bijective, $f\cdot f=id$, e.g. xor with a constant). $g$ is a idempotent mapping choosing an arbitrary representative ...

### 4 Does this “set intersection” problem have a different name?

1 answers, 66 views np-complete sets
I've been back and forth about this one. I have the following theoretical homework problem, which describes the SET-INTERSECTION problem. In my homework, it's ...

### 2 What is the deterministic time complexity of obtaining the set of distinct elements?

0 answers, 50 views time-complexity sorting sets hashing
Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we have can read, write and compare them in O(1) time with arbitrary positions). What's ...

### 6 Is the intersection of infinitely many recursive sets recursive?

2 answers, 771 views computability sets
Is the intersection of infinitely many recursive sets $\bigcap_{i}U_{i}$ (where each set is different ) recursive? Recursively enumerable? I know the union need not be recursive, because deciding if ...