A question in some formal system with a yes-or-no answer.

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1answer
58 views

How do you know a problems is non-computable?

I am currently looking at intractable problems and N/NP etc but am a little confused about one term used in the book I am reading. It says in this book that a non computable problem is one which ...
1
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1answer
43 views

Can the decision version of an optimization problem in NP, be in P?

It is well known that a optimization problem can be turned into a decision problem with an extra parameter: e.g. in TSP we are looking for the lowest cost for a tour, the decision version therefore ...
0
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1answer
40 views

show that special case of NP-complete problem is also NP-complete?

I want to show that a problem is NP-hard by reducing a known NP-complete problem to it. However, I will have to use a special case of the NP-complete problem for the reduction to work. I'm pretty sure ...
2
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3answers
56 views

Proof that whether a regular language is finite is decidable

I have this question for a homework. The question stems from the fact that you can determine whether a regular language is empty by using a Turing machine to count the states n in the given FSM. When ...
0
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0answers
18 views

turing machine decidability language

I must show that this language is decidable but I think it's not {D, Ρ} | D is a DFA and P is a ΡDA which L(D) ∩ L(Ρ) = ∅ } Here what I think I give a reduction from E(TM). I suppose that this ...
1
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1answer
45 views

What is the name of the word problem for free groups under straight line program encoding?

I believe that the word problem is the problem to decide whether two different expressions denote the same element of a suitably defined algebraic structure. For simplicity, let us focus on free ...
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0answers
28 views

Satisfying two constraint with an oracle for satisfying one

Given an oracle to solve the knapsack feasibility problem: $$a^Tx=b, \ x \in \mathbb{N}^n $$ How can one solve in polynominal time the problem of satisfying two constraints at the same time?
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1answer
55 views

Reduce set partition search to decision?

I'm a little lost and don't know how to approach this problem. Show the partition search problem can be poly-time reduced to the partition decision problem, the partition decision problem takes ...
3
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2answers
121 views

Why classification represents all computations?

I'm a computer science student taking a theory of computation class. Recently we were taught about what is computable and what is not and about the Turing machine. As I understood (please correct me ...
7
votes
3answers
787 views

Undecidability of telling if a program returns true or false

Consider the problem of taking an input Turing machine and determining if the final cell is a $0$ or $1$ after computation halts. On cases where it writes something else or does not halt, you are ...
1
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1answer
56 views

Metaheuristic for NP-complete problem without exact algorithms other than brute-force

Computing Pure Nash Equilibria (PNE) is a Game Theory related problem. Deciding if there exists PNE in a given game has been shown to be NP-Complete (Gottlob et al.). I want to design a metaheuristic ...
0
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1answer
31 views

Reduce knapsack to problem with {0,1}-Matrix

I'm looking for a problem, where i can reduce the knapsack feasibility problem: $$a^Tx=b,\ \textbf{with} \ a\in \mathbb{N}^n,b \in \mathbb{N}, x \in \{0,1\}^n$$ to a problem, where i have a matrix ...
3
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1answer
19 views

Maximal class for which function equivalence is decidable

I previously asked if it's decidable whether two primitive recursive functions are equivalent: "primitive recursive functional equivalence". The answer was no. Here is my followup. What is the most ...
4
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2answers
40 views

primitive recursive functional equivalence

Given two primitive recursive functions is it decidable whether or not they are the same function? For example lets take sorting algorithms A, and B which are primitive recursive. While there are many ...
1
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2answers
40 views

Proof that MAX CLIQUE is NP-Hard

My question is simple: does any body know where can I find the proof that MAX CLIQUE is NP-HARD? Remarks: MAX CLIQUE is the decision problem defined as follows:Given a graph $G$ and $k>0$. Does ...
0
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1answer
30 views

On submultisets of given cardinality and bound that sum to $0$

Given multiset of integers $a_1,\dots,a_{m}$ where $|a_i|\leq\log^cm$ for some $c\in\Bbb R^+$. Is it $\mathsf{NP}$-complete to decide if there is a cardinality $\lceil m^\alpha\rceil$ submultiset for ...
0
votes
1answer
26 views

DP - Removing contiguous subsequences from a sequence optimally

I was asked this question a while ago and I'm very stuck: You have a sequence of 0's and 1's, and you can perform one ...
1
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1answer
47 views

Equivalence of regular grammars

I know that proving context free grammars equivalent is undecidable. I also know that proving if a context free grammar recognizes a regular language is undecidable. Here is my question: is proving ...
8
votes
0answers
190 views

Is the halting problem decidable for 3 symbol one dimensional cellular automata?

I've been trying to figure out if the halting problem is decidable for 3-symbol one-dimensional cellular automata. Definition. A cellular automaton has halted in state $s$ if running the automaton on ...
1
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1answer
21 views

restricted sub-permutations check

I am solving the following problem, motived by combinatorial optimization sampling proces. I have restriction (0,1) matrix to restrict which item (column index) can be on current position (row index) ...
5
votes
0answers
48 views

Turing reductions by NX ∩ coNX and binary relation problems

Let $A$ be a non-deterministic algorithm computing a binary relation between an input string and possible output strings. Let NX be a (potentially non-deterministic) complexity class. What is a good ...
2
votes
1answer
55 views

How exactly does a Max 2 Sat reduce to a 3 Sat?

I've been reading this article which tries and explains how the max 2 sat problem is essentially a 3-sat problem and is NP-hard. However, if you see the article, I'm not able to understand why, after ...
3
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1answer
48 views

Is the word problem for regular languages in ALogTime?

Given a regular language (by a sparse or dense matrix describing the graph of the NFA) (initially the description was supposed to be a regular expression) and a word, can the problem whether the word ...
5
votes
2answers
123 views

Will encoding affect computability?

I think this question arises from not having a clear idea on encoding. So, If I have a problem intuitively there may be many ways of encoding it using TM's alphabet set. Slight variation in the ...
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0answers
46 views

Showing that $H'$ is not semi-decidable

I have an introductory class in computability theory and I'm currently working on my first exercises. I'm wondering if I'm on the right track with proving undecidable languages. Could you please have ...
3
votes
1answer
52 views

How do POMDPs and Dynamic Influence Diagrams differ?

To give some perspective, first consider the following diagram comparing Markov Chains, HMMs, MDPs, and POMDPs (I'm not sure who to credit for it). Fully observable ...
6
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1answer
78 views

What NP decision problems are not self-reducible?

So we just learned about self-reducibility in class. My professor and our textbook would not commit to saying that all problems in NP are self-reducible, but there didn't seem to be any examples of ...
11
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2answers
816 views

Is Post Correspondence Problem in NP?

I just read some pages in Sipser's book Introduction to Theory of Computation about Post Correspondence Problem, and I'm thinking that PCP is actually in NP. The certifier is: for an input ...
7
votes
1answer
120 views

Understanding of Turing's Answer to the Entscheidungsproblem

I apologize if this question has been asked before, but I was not able to find a duplicate. I have just finished reading The Annotated Turing and I am a bit confused. From what I understand, the ...
0
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1answer
105 views

Are “TM M accepts some string of length greater than 100” and “TM M accepts some string of length at most 100” decidable?

I have two questions as in the title: TM M accepts some string of length greater than 100 TM M accepts some string of length at most 100 Since 1. is infinite, we can rephrase question as "does TM ...
2
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0answers
89 views

Determining whether a number is a perfect square without computing its square root

One of the interesting results of Number Theory is the theory of quadratic reciprocity. One finds that it is possible to determine whether an equation $x^2 \equiv a \pmod p$ has a solution $x$ without ...
1
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1answer
130 views

Does a path exist going through each color only once?

I have a directed, colored graph (each node has a color), and I want to find if a path from node A to node B exists such that the path goes through each color at MOST once. I think this problem can ...
6
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2answers
202 views

Is there any strategy to brute force search?

I don't know how to state it elegantly, but basically, I want to implement a brute force search algorithm, but there are many different ways that I could enumerate through the search space. This ...
5
votes
2answers
131 views

How does one find out whether $N = a^b$ for some $b$?

I was trying to find out how to find whether $N$ is a perfect power or not for some $a$ and $b$ (so the algorithm should discover that its not a perfect power if its not expressable in the form ...
1
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0answers
76 views

Proving NP-Completeness by reduction

I'm given a more restricted version of 3-SAT called 3-SAT-M: Problem: 3-SAT-M INPUT: A set of clauses C {c1,...,ck} over n boolean variables {x1,...,xn}, where every clause contains ...
1
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1answer
85 views

Q: Is chess game movement TM decidable?

If we have a finite chess board and two figures x and y. Is it possible to get y from x by following chess rules and when white is y and white starts from y placement. Is this decidable? My ...
3
votes
1answer
44 views

Efficient algorithm for determining if $\pm c_1 \pm c_2 \dots \pm c_n = 0$

Suppose that we're given $n$ integers $c_1, c_2, \dots, c_n$. We want to know if there is any assignment of $+$ and $-$ signs such that $$ \pm c_1 \pm c_2 \dots \pm c_n = 0. $$ Does anyone ...
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0answers
40 views

What are some results for non-trivial lower bounds for the time complexity of decision problems?

Typically decision problems are studied in complexity theory and function problems are studied in the Analysis of Algorithms. Unfortunately, Complexity Theory tends to abstract over the exact time ...
1
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2answers
235 views

If an NP-complete problem is shown to have a non-polynomial lower bound, would that prove that P != NP?

I understand that the Cook-Levin theorem proved that any NP problem is reducible to an NP-complete problem, which signifies that if a polynomial-time algorithm for an NP-complete problem is found, it ...
2
votes
1answer
98 views

How are these problem variants that ask about the size of optimal solutions in NP?

I just started reading Vazirani's book "Approximation Algorithms". It is legally available online here. On page 5 (23 in the pdf), it says that the following decision problems are in NP: Is the ...
0
votes
1answer
256 views

Clique decision problem restricted to a subgraph [closed]

I know that the clique problem is NP-complete. However, what if we change the problem a little bit? For example, Given a graph $G(V,E)$, an integer $k$ and a subset $S$ of $m$ vertices, we are ...
4
votes
0answers
55 views

Proof that P is closed against switching between polynomially related encodings

Lemma 34.1 Let $Q$ be an abstract decision problem on an instance set $I$, and let $e_1$ and $e_2$ be polynomially related encodings on $I$. Then, $e_1(Q)\in \mathrm{P}$ if and ...
1
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1answer
101 views

NP Complete Subset GCD Proof

$SubsetGCD$ is described by the following: instance: A set of positive integers $S$ and an integer $k$ question: does there exist a subset $S'$ of $S$ of size $k$ such that $GCD(S') = GCD(S)$ ...
2
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1answer
87 views

Determine if items can be ordered grouping two simultaneous criteria

For a set of items with two properties, how can it be detemined if they can be ordered in a way so that for every value of either property all items of that value are grouped together. Obviously ...
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1answer
78 views

Why decision problem definition ignores Gödel incompleteness theorem?

The following question assume that the decision problem definition (syntactic) has been written (and could be changed if it isn't able) to catch a concept (meaning, semantic) which has both nice ...
3
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0answers
63 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 $f(x)$ ...
3
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1answer
31 views

Extended version of the theory of reals and its decidability

It is well-known due to Tarski that the theory of reals $(\mathbb{R},+,\cdot,<,=)$ is decidable. I was asking my self whether one would lose the decidability by adding all real constants. More ...
3
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4answers
2k views

Language of Turing machines that loop on all inputs, recognizable?

Prove that the language Loop Turning Machine = { < M > | M is a TM that loops on all inputs} is recognizable. I feel like $M$ would never halt. To make $M$ recognizable it needs to accept or ...
1
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1answer
321 views

If the decision problem can be solved in poly time, show the optimization problem also can [duplicate]

Here is a problem I am trying to solve: The bin packing decision problem is defined as follows: given an unlimited number of bins, each of capacity equal to $1$, and $n$ objects with sizes ...
3
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1answer
18 views

Extension of Tarski's result on the decidability of reals

Due to Tarski's result, it is well-known that the first-order theory of reals $(\mathbb{R},+,\cdot,<,=,0,1)$ is decidable. I am working on a paper where I need an extension of this result. More ...