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0answers
12 views

Characterizing the range of a polytime function

Is it true that an infinite language is in P iff it is the range of a length increasing polytime function? I ask because I know that it is a basic result in computability theory that a set is ...
0
votes
0answers
58 views

Clique and its algorithm

The problem: Input: A graph $G=(V,E)$ and a number $k$ Question: Does G have a k-clique, i.e. a complete subgraph of k vertices? If we were suppose to solve, the function problem that a given graph ...
0
votes
1answer
22 views

If A is polynomial time reducible to B such that B <= A, does it mean B must be a polynomial time algorithm?

I don't understand what it means for A to be polynomial time reducible to B. I'm guessing is that we can revised the algorithm some how such that it becomes B, where B is a polynomial time algorithm. ...
2
votes
1answer
117 views

task scheduling optimization problem

I'm interested in such problem. I have a set of $n$ tasks ${T_i}$ and directed acyclic graph, which nodes correspond to tasks and edges correspond to order of execution two tasks. In other words if I ...
1
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3answers
55 views

If A is in P and B is non-trivial, then A ≤p B [duplicate]

On wikipedia's article on Polynomial-time reduction it states: Every nontrivial decision problem in P (the class of polynomial-time decision problems, where nontrivial means that not every input ...
0
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1answer
37 views

Vertex Cover of size k in a tree?

What is a polynomial time algorithm for finding a vertex cover of size $k$ in a tree? Would depth first or breadth first search be efficient or is there some other algorithm that finds the vertex ...
3
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1answer
23 views

What does the 2 in a 2-approximation algorithm mean?

Does the 2 in a 2-approximation algorithm mean the solution is within 2*OPT or OPT/2?
2
votes
1answer
82 views

Find a subgraph whose edge weights sum to at least the number of nodes

Given a graph G = (V,E) every edge is assigned a real number Xe $\in$ [0,1] The sum of x variables for all edges is equal to the number of edges -1 : $\sum x_V = |V|-1$ For a subset S ...
4
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0answers
35 views

Polynomial time algorithms on strings [closed]

I am looking for familiar problems on strings of finite length over an finite alphabet, where a polynomial time algorithm is known. To be more precise, let $\Sigma$ be a finite alphabet. I am looking ...
-1
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1answer
26 views

polynomial time reduction of 2 langauges

If we can reduce a language y to x. x ≤P y how do I prove x(complement) ≤P y (complement)
2
votes
1answer
32 views

Polynomial Time Reduction - Does 0 calls to the black box still imply a reduction?

Using the following definition: Reduction: There is a polynomial-time reduction from problem $X$ to problem $Y$ if arbitrary instances of problem $X$ can be solved using: Polynomial ...
2
votes
0answers
17 views

Simulate NPDAs with DTMs using only polynomial overhead

We know by polynomial-time parsing algorithms like the classical CYK algorithm that $\mathrm{CFL} \subseteq \mathrm{P}$. Furthermore, it is easy to show by direct simulation that $\mathrm{DCFL} ...
2
votes
1answer
19 views

Are there FPTASs for the min cost flow problem?

In literature, one can find many approximation algorithms for the multicommodity min cost flow problem or other variants of the standard single-commodity min cost flow problem. But are there FPTASs ...
5
votes
3answers
320 views

3SAT analogous problem in P

Is there a problem like 3 SAT like problem in P where if we find an algorithm for this problem, we can solve all problems in P? For instance if we solve this problem in P, may be we can solve prime ...
2
votes
1answer
81 views

Are there any coP problems

Is there a notion of coP problem? Also is there a notion of every problem being reducible to one problem in P (like 3SAT in NP completeness)?
4
votes
4answers
482 views

How can an algorithm have exponential space complexity but polynomial time complexity?

For enumerating the minimal feedback vertex sets of a graph Schwikowski and Speckenmeyer show an algorithm "GENERATE-MFVS" in their publication "On enumerating all minimal solutions of feedback ...
2
votes
1answer
37 views

Proof of P-Hardness by reduction

I want to proof the P-Hardness of a language. Why is it enough to make a reduction-proof from an other, already P-Complete known language?
4
votes
1answer
50 views

Understanding the Sipser-Gacs-Lautemann theorem

The class $BPP$ contains all the languages decided by a probabilistic Turing machine in polynomial time with probability of success more that 2/3 for every input. The class $\Sigma^p_2$ contains all ...
2
votes
1answer
47 views

Why is Ibarra Kim for 0/1 knapsack an fully polynomial time approximation scheme (FPTAS)?

According to one of my CS lectures, there is an fully polynomial time approximation scheme for the 0/1 Knapsack problem. A first version was developed by Ibarra and Kim, but there are several improved ...
3
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0answers
25 views

Finding a perfect matching using an LP

I have a basic question about the power of Linear Programming that has been bothering me for some time. I believe there is something simple I am missing. Linear Programming is $\mathsf{P}$-complete, ...
4
votes
1answer
100 views

Complexity of Linear Diophantine equations

My question is simply, can linear Diophantine equations be solved in polynomial time? Specifically, I am looking at equations of the form $a_1 x_1+a_2 x_2 + ... + a_n x_n = k$, where $a_i,x_i,k$ are ...
4
votes
1answer
132 views

Complexity of the decision version of determining a min-cut

I was wondering what the complexity of the following problem is: Given: A flow network $N$ with a source $s$, sink $t$ and a number $k$. Question: Is there an $s$-$t$ cut of capacity at most ...
3
votes
1answer
71 views

A Reduction from XORSAT to 2-SAT

Does anyone know of a non-trivial reduction from XORSAT to 2-sat since they are both in P? (By non-trivial I mean one that does not just solve the instance of XORSAT and map it to a fixed instance of ...
3
votes
1answer
83 views

Finding number not in list with wildcards

I have a list like this: 1*0*0 1**0* 0*0** 001** Where the number of elements in each row is $n$ and * is a wildcard for 0 or 1. I need a polynomial-time ...
4
votes
1answer
77 views

Unary in $P$, binary not in $P$

I would like to know if there is a known decision problem with the following characteristics: Represented in unary, the problem is decidable in polynomial time. Represented in binary, the problem is ...
-1
votes
1answer
43 views

Is P^SAT subset of sum of NP and co-NP

I have a following problem: Let $P^{SAT}$ be a class of problems decidable by a deterministic polynomial Turing Machines with SAT oracle. (only one question to oracle). Assume that: $co-NP \neq NP ...
5
votes
0answers
65 views

A matrix rank problem over finite fields

I have already asked a similar question here, but since I have not got an acceptable answer, I decided to ask a simpler version of the question here. Let $M|\mathbf w$, where $M$ is a matrix and ...
3
votes
4answers
989 views

How to prove that problem is not in P

Given some abstract problem how can I prove that this problem is not in P. I mean, what is the method for proving such thesis?
2
votes
1answer
36 views

A variant of the set cover problem: Is that a known problem?

Can this problem be solved in poly time? Input: $S_i \subset \{1,\cdots,n\}$ for $i=1,\cdots, n$. Question: Is it possible to select an $a_i \in S_i$ for each $i=1,\cdots,n$, such that ...
1
vote
3answers
79 views

NP-completeness: Reduce to or reduce from?

Very simple question, but a mistake I make often enough that I'd love to have a standard reference. I'm showing that a problem $P$ is NP-Hard by assuming I have a polynomial time algorithm to solve ...
3
votes
3answers
357 views

Can't understand why the DP Subset Sum algorithm is not polynomial

I can not understand why the dynamic programming algorithm for the Subset Sum, is not polynomial. Even though the sum to find 'T' is greater than the total sum of the 'n' elements of the set , the ...
0
votes
1answer
47 views

Is polynomial time reducibility reversible?

If a language $A$ is reducible to some language $B$, does it follow that $B$ is reducible to $A$? My guess is no, it having something to do with the function $f$ in the definition of $A$ reducing to ...
0
votes
1answer
36 views

Complexity of general polynomial map evaluation is polynomial?

A polynomial map is equal to another polynomial map iff they take on the same values at each point. So this is different from formal polynomials. So since in $\Bbb{Z}_p$, $x^{p-1} = 1$ for all $x ...
3
votes
2answers
304 views

How to determine if a black-box is polynomial or exponential

I have a problem which essentially reduces to this: You have a black-box function that accepts inputs of length $n$. You can measure the amount of time the function takes to return the answer, but ...
2
votes
1answer
60 views

How to optimally seperate a student body?

Students will identify certain students they want to work with. I have therefore decided to split them into two groups where I want to minimize the number of people in Group 1 who want to work with ...
2
votes
1answer
29 views

Polynomial hierarchy intersection

While familiarizing myself with polynomial hierarchy, I have come across a problem of showing $NP^{\Sigma_{k}^{p} \cap \Pi_{k}^{p}} \subseteq \Sigma_{k}^{p}$. By looking at the proof for $NP^{SAT} ...
2
votes
1answer
44 views

Polynomial Hierarchy — polynomial time TM

Consider, for example, the definition for $\Sigma_2^p$ complexity class. $$ x \in L \Leftrightarrow \exists u_1 \forall u_2 \;M(x, u_1, u_2) = 1, $$ where $u_1, u_2 \in \{0,1\}^{p(|x|)}$, for some ...
1
vote
1answer
37 views

Is P closed under subwords? [closed]

Given a language $L\subseteq \Sigma^*$ in $P$, is the language $subwords(L) = \{v\in\Sigma^* : \text{there exist } u,w\in \Sigma^* \text{ with } uvw\in L\}$ that consists of all subwords of words ...
1
vote
1answer
95 views

Relation between logspace-uniform circuits and P-uniform circuits

In the book "Computational complexity" of Barak and Arora, on page 112, they state that: Theorem 6.15: A language has logspace-uniform circuits of polynomial size iff it is in P. The proof of ...
0
votes
1answer
65 views

What's the difference between “polynomial time Turing-reducible” and “polynomial time many-to-one reducible”? [duplicate]

The following definitions are from Li, M., & Vitányi, P. (1997). An introduction to Kolmogorov complexity and its applications (2nd ed.), pg. 38. A language $A$ is called polynomial time ...
0
votes
1answer
147 views

Does two languages being in P imply reduction to each other?

Given two languages $L_1$ and $L_2$ that are in $\mathsf{P}$, can it be proven that there is a polynomial time reduction from $L_1$ to $L_2$ and vice versa? If so, how? I noticed that if $L_1$ is the ...
1
vote
2answers
162 views

P vs NP: Assuming P = NP

Lets assume $P = NP$. Can we say if every language $L \in P$, then $L \in NPC$? I read $P \subseteq NP$, which means that $L\in NP$. So I know for example, that a language can be $NP \text{ hard}$, ...
1
vote
1answer
243 views

how to solve NFA acceptance problem in polynomial time

I need to show that the language Anfa = {(A,w)| A is an nondeterministic finite automata that accepts w} can be decided in polynomial time. My problem is every solution that I think of requires ...
7
votes
4answers
182 views

Problems that are NP but polynomial on graphs of bounded treewidth

I heard here that the Hamiltonian cycle problem is polynomial on graphs of bounded treewidth. I am interested in examples/references to different problems which is essentially hard but having ...
1
vote
1answer
515 views

Is the set partitioning problem NP complete?

I know that the set partitioning problem defined like this: Given $S = \left\{ x_1, \ldots x_n \right\}$, find $S_1$ and $S_2$ such that $S_1 \cap S_2 = \emptyset$, $S_1 \cup S_2 = S$ and $\sum_{x_i ...
2
votes
1answer
123 views

Time complexity of languages that are polynomial time reducible to NP complete languages

I am wondering if given the time complexity of an NP-Complete problem or at least some information about it for example if $ SAT\in Time(2^{sqrt(n)})$ (hypothetically) could I assume that all ...
3
votes
1answer
230 views

Is the set-partition problem polynomial time reducible to the subset-sum problem?

There are many solutions on the web showing that the subset-sum problem is polynomial time reducible to the set-partition problem. However, during my search, I came across the following powerpoint ...
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1answer
376 views

Proving that the complexity class $P$ is closed under union

The following is my proof for $P$ being closed under union. I wish to know if my proof is correct in addition to what it means for the union of two problems. Proof: Let $p_1, p_2 \in P$ Then by ...
0
votes
0answers
144 views

Proving languages are complete on NL?

I'm trying to prove that every language that is not the empty set or {0,1}* is complete for NL (nondeterministic logarithmic space) under polynomial-time Karp reductions. I'm really not sure how to ...
2
votes
1answer
212 views

Is it possible to solve parity game problem in polynomial time?

Is it practically possible or even near possible to make parity game to be solved in polynomial time? If yes, how? and if No, why?