Questions about finding mappings between problems that allow solving one problem using a solution of another one.

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0
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1answer
56 views

Checking acceptance of a word vs finding an accepted word

We know that checking whether some word w is accepted by a turing machine TM is undecidable. But what about the problem of finding one accepting word of a TM? Are these two problems related in some ...
-1
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0answers
31 views

Reduction NP-Complete with graph undirected [duplicate]

Given a graph undirected $G=(V,E)$ a subset $I$ of $V$ is indipendent for each couples of vertices u,v in $I$ and {$u,v$} is not in $E$. Prove that the language $L$={$<G,k>$: $k$ is a positive ...
-1
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0answers
51 views

Questions on the proof of Rice's theorem

I am trying to understand the proof of Rice's theorem. I read it in Sipser and here. The theorem is Let $P$ be any non-trivial property of languages of Turing machines. Then, the following ...
1
vote
1answer
44 views

Do problems in P only reduce to NP and coNP problems?

Consider the languages $B,C,D$, such that $B\le_p C$ and $B\le_p D$. Statement: $B\in P, D\in NP, C\in coNP$. Is the statement true for every $B,C,D$? I know that the answer is no and I have ...
1
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2answers
48 views

$A$ is finite, $B$ is NPC - When there's a polynomial reduction from $A$ to $B$?

$A$ is finite, $B$ is NPC - When there's a polynomial reduction from $A$ to $B$? Basically, I've understood that if $A$ is finite, then there's a reduction for every $B$ which isn't trivial ...
0
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0answers
29 views

mapping reduction for every recursive language [duplicate]

how do I prove that for every 2 languages $A,B\in R$ where $A,B \notin \{ \emptyset , \Sigma^* \}$ I can do a reduction $A \leq_m B$? [EDIT] My try: $A$ is decidable therefore it has a turing ...
-1
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0answers
27 views

How can I prove that Clique Problem is NP-complete using TSP

I would like to know if there is a way to prove that Clique problem is NP-Complete, using TSP. In order to prove that Clique is NP-Complete, I know that first I have to prove that Clique is NP. Then ...
5
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1answer
106 views

Could min cut be easier than network flow?

Thanks to the max-flow min-cut theorem, we know that we can use any algorithm to compute a maximum flow in a network graph to compute a $(s,t)$-min-cut. Therefore, the complexity of computing a ...
3
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0answers
39 views

Why are decision problems easier than the equivallent optimization problems?

Suppose that we have an optimization problem defined as follows: $OPT$ = Given an input string defining a set of feasible solutions $F$ and an objective function $f$, find $x\in F$ maximizing $f(x)$ ...
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0answers
27 views

reduction from knapsack to 3-SAT

I need a help on how to reduce the knapsack problem to 3-SAT ? I already tried to do it and searched on the net, but I did not find anything.
7
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0answers
36 views

Are there any known AM-complete problems/is AM-complete well defined?

I'm curious about whether there are any complete problems in the Arthur-Merlin complexity class. Graph Non-Isomorphism (GNI) seems to be the canonical example of a problem in AM, but it's probably not ...
2
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1answer
46 views

Relation between the “Point-Cover-Interval” problem and the “Interval Scheduling” problem

Point-Cover-Interval Problem: Given a set $\mathcal{I}$ of $n$ intervals $[s_1, f_1], \ldots, [s_n, f_n]$ along a real line, find a minimum number of points $P$ such that each interval contains ...
2
votes
1answer
59 views

Prove Vertex-Cover of maximum degree 3 is NPC

This is a homework question. I need to prove that the following language is in NP Complete: 3-VERTEX-COVER = $\{\langle G,k\rangle \mid$ G is an undirected graph, each vertex in $G$ has at most ...
-1
votes
1answer
63 views

Determine if the language is $R$

Consider the following language: $$L = \{ \langle M \rangle \ |\ M \text { is a TM that decides the halting problem} \}$$ determine whether or not the language is in $R$. Now, from my ...
0
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3answers
62 views

Reduction and decidability

Consider the following language: $$ L = \{ \langle M \rangle \ |\ M \text { accepts } w \text { whenever it accepts } w^R \}$$ I am trying to understand the following proof that this language $L$ is ...
2
votes
1answer
53 views

Cycles in hardness of ST-CON for the class NL

It seems to me that the problem of $s$, $t$ connectivity in a DAG should still be NL-Complete. I am aware that ST-CON without the DAG restriction is complete for NL, so obviously the DAG restriction ...
3
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0answers
49 views

smallest satisfiability-equivalent formulas (generalized Tseitin transform)?

What is known about the following optimization problem for formulas in propositional logic: input: formula $F$ output: formula $G$ in CNF with $\mathrm{Var}(G) \supseteq \mathrm{Var}(F)$ such that ...
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votes
1answer
56 views

If an NP problem reduces to an NPC problem, it is NPC?

Is the following statement true? If a problem P1 is in NP and polynomial time reducible to P2, where P2 is NP-complete, then P1 is also NP-complete. Intuitively I think the answer is No because ...
0
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1answer
29 views

Reduction of Circuit Satisfiability to CNFSAT [duplicate]

CNFSAT is Karp reducible to Circuit-SAT by replacing all the conjunctions with AND gate, disjunctions with OR gate and negations with NOT gate. However, if we apply the same approach to Karp reduce ...
2
votes
1answer
80 views

Reduce our problem to a known np-complete problem

Subgraph isomorphism We have the graphs $G_1=(V_1,E_1), G_2=(V_2,E_2)$. Question: Is the graph G_1 isomorphic with a subgraph of $G_2$ ? (i.e. is there a subset of vertices of $G_2, V \subseteq ...
1
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1answer
38 views

np-complete proof, turing reduction

I have some difficulties with a complexity proof : I work with 3 problems : A, B and C I know : A-> B A-> C C -> B A-> B meaning : if I have a "yes answer " for A , then I have a "yes answer" for ...
2
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0answers
182 views

PSPACE completeness, with different kinds of reductions [closed]

PSPACE-complete$_{FP}$ problems are the PSPACE problems such that every other PSPACE problem can be transformed to it with a polynomial time reduction, i.e. the reduction is an algorithm $\in$ FP. ...
5
votes
1answer
114 views

Reduction from Vertex Cover to Polygon Cover

Polygon Cover: Input: A set of points $P$, a set of polygons $S$ in a 2D plane, and a positive integer $k \in \mathbb{N}$. Output: True if and only if there exists a subset in $S$ of at most $k$ ...
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1answer
47 views

Proof of Circuit-Sat to Nand-Sat polynomial time many–one reducibility

Given a gate called Nand with the following truth table: A | B | A Nand B ------------------ 0 | 0 | 1 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 We can ...
0
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1answer
52 views

Poly-time reduction: D and D Comp [duplicate]

Looking at the Independent Set problem and its complement, I want to show that IS is poly-time reducible to its complement, however I am struggling on coming up with the reduction function. I will ...
0
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0answers
32 views

Reducing a Knapsack-type problem to a known problem

The Quadratic Knapsack problem, introduced by Gallo, is an optimization problem in the following form: $max \sum_{i=1}^n{\sum_{j=1}^n{q_{ij}x_ix_j}}$ $s.t \sum_{i=1}^n{w_ix_i} \leq c$ $x \in \{0, ...
1
vote
1answer
89 views

P-Completeness and Reducibility

I am taking an algorithm analysis class and am stuck on one of my homework problems and would appreciate it if I could receive some guidance. The problem I'm stuck on is proving that the empty ...
0
votes
1answer
170 views

Proving a language is not Turing-recognizable by reduction

I'm having a really hard time understanding some of these concepts. I've read them over from several different sources and still can't reach the a-ha moment. I need to prove a language L is not ...
3
votes
3answers
390 views

The relation between 2SAT and 3SAT

Show that proving 2SAT is not NP-Complete would prove that 3SAT is not in P. Or eqivalently - Show that proving 3SAT is in P would prove that 2SAT is NP-Complete. I can see there is an ...
3
votes
2answers
74 views

Restricted Integer Programming

The integer feasibility problem is NP-complete: $Ax=b, x \geq 0, x \mbox{ integer}$ $A$ contains elements in $\mathbb{R}$ If we restrict this: $A$ contains only elements in: $\{1,0\}$ ...
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2answers
81 views

If $B$, $\overline{B}\neq \varnothing$ , then for every recursive set $A$, $A \leq_m B$

How to prove if $B$, $\overline{B}\neq \varnothing$ , then for every recursive set $A$, $A \leq_m B$ ? it means every recursive set is mapping reducible to set $B\neq \aleph$. I really have no idea ...
1
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2answers
49 views

Is it true, If $A$ is turing recognizable and $A \leq_m\bar{A}$ then $A$ is recursive?

If $A$ is turing recognizable and $A \leq_m\bar{A}$ then $A$ is recursive? If it is true how to prove it? Update It is my attempt, If $A$ is turing recognizable (r.e.) and $\bar{A}$ is r.e. then ...
3
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1answer
36 views

Methods of turning a decision problem into finding the certificate?

I usually find this in the context of asking about NP-complete problems, but any decision problem works. We start by assuming there's a polynomial time algorithm that gives the yes or no answer. If ...
1
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0answers
109 views

Is the language of Turing Machines that halt on every input recognizable?

I am trying to reduce the complement of the HALTING problem (WLOG, the complement of the HALTING problem is the language of TMs that loop on some string w)to this language in order to show that it is ...
2
votes
1answer
86 views

Reduction to $n\log n$ time problem

If a problem $A$ is poly-time reducible to a problem $B$ ($A <_\mathrm{p} B$), and $B$ can be solved in time $O(n\log n)$, can $A$ also be solved in time $O(n\log n)$?
0
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1answer
125 views

Polynominal reduction from unbounded knapsack problem to general integer programming

Given an oracle that can solve in polynominal time: $$a^Tx=b$$ $$x \geq 0$$ So it can solve the feasibility problem with one equality-constraint(a is here a vector and b is a constant, x is required ...
2
votes
0answers
51 views

Ideas on reducing Traveling Salesman to Metric Traveling Salesman?

I want to show a polynomial reduction from TSP to Metric TSP. I know the rule is: $(G, k) \in TSP \iff (G', k') \in MTSP$ where $G$ is some graph, and $k$ is some bound. It seems like whatever I map ...
2
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1answer
48 views

Linear and almost-linear perfect hashing

I am trying to understand the sentence from a paper by Patrascu: Unfortunately, we do not have linear perfect hashing. Instead, we use a family of hash functions.... with almost-linearity The ...
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votes
1answer
89 views

Let A,B be languages. If A is decidable and B undecidable, then A reducible to B

So I'm learning for an upcoming exam and there's a specific problem which I can't show: Let A be decidable and B undecidable, then $A \le B$ Can someone give me a hint how to solve that? ...
3
votes
3answers
258 views

4-color to 3-color polynomial reduction

I know a simple reduction from 3-color to 4-color. But how do you reduce 4-color to 3-color ? I have been searching for the right way to make this reduction for a while now. I would love some ...
3
votes
1answer
183 views

Variants of the 3-SUM problem

The 3SUM problem has two variants. In one variant, there is a single array $S$ of integers, and we have to find three different elements $a,b,c \in S$ such that $a+b+c=0$. In another variant, there ...
2
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2answers
64 views

Logical Reduction

Reducing one computable problem to another by providing an algorithm which transforms an instance of one problem to one of the other (and limiting the time or space of that algorithm) is clear to me. ...
2
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0answers
50 views

What is the trick of “adding a huge number” for in the reduction from $\textsf{3-Partition}$?

Problem: To prove the $\textsf{NP-Completeness}$ of the problem of "Packing Squares (with different side length) into A Rectangle", $\textsf{3-Partition}$ is reduced to it, as shown in the following ...
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0answers
13 views

Solving $Isomorphism$ using $AUTOM$ in polynomial time

Let $Iso$ be the language of all $<G,H>$ such that $G$ and $H$ are isomorphic, and $AUTOM$ be the language of all $G$'s such that $G$ has a non-trivial automorphism. I'd like to show that, ...
3
votes
2answers
23 views

$3EQ \leq _P 2EQ$

Let: $2EQ$ - The language of all binary ($\mathbb{Z}_2$) equation sets that have a solution in $\mathbb{Z}_2$, where each multiplication is of at most two $x_i,\, x_j$. Meaning a set of equations of ...
2
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0answers
34 views

What are the fundamental principles/algorithms on the process of equation solving?

I have seen a lot of solvers that are capable of, for example, getting an equation such as x ^ 2 + x = 12 and finding x = [3, -4]. I know some of them are implemented by hardcoding special cases. For ...
1
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1answer
43 views

Reduce Clique to Vertex Cover

I read on the internet that it's possible to reduce Clique to Vertex Cover. Almost everyone use this theorem: if a graph $G$ has a clique of size $k$ then the complement of $G$ has a vertex cover of ...
1
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1answer
41 views

SAT-3CNF - Clique [closed]

Could someone show me ( or give me a valuable hint) how to reduce k-Clique problem to SAT-3CNF problem ? I am able to prove reduction from SAT-3CNF to k-Clique, but in the opposite direction it's ...
2
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0answers
36 views

reduction of maxcut problem

Show that if the MAX CUT decision problem can be solved in polynomial time so can the MAX CUT optimization problem by writing an algorithm that solves the optimization problem using an algorithm for ...
2
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1answer
56 views

Reduction from a further constrained problem

If I find an NP Hard problem that is equivalent to my problem with an additional constraint or bound, can I still prove that my problem is NP Hard? Generally, this is probably not the case. For ...