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Questions tagged [decision-problem]

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

559 questions
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Is legislation NP-complete?

I would like to know if there has been any work relating legal code to complexity. In particular, suppose we have the decision problem "Given this law book and this particular set of circumstances, is the defendant guilty?" What complexity class…
Gaslight Deceive Subvert
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Optimization version of decision problems

It is known that each optimization/search problem has an equivalent decision problem. For example the shortest path problem optimization/search version: Given an undirected unweighted graph $G = (V, E)$ and two vertices $v,u\in V$, find a…
bek
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Why isn't this undecidable problem in NP?

Clearly there aren't any undecidable problems in NP. However, according to Wikipedia: NP is the set of all decision problems for which the instances where the answer is "yes" have [.. proofs that are] verifiable in polynomial time by a…
BlueRaja - Danny Pflughoeft
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Distinguish Decision Procedure vs SMT solver vs Theorem prover vs Constraint solver

Those terminologies confuse me. As I understand SAT solver: decide the satisfiability of propositional logic (using DPLL or Local Search). Decision procedure is a procedure to decide the satisfiability of a certain decidable first-order…
sean
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How is the traveling salesman problem verifiable in polynomial time?

So I understand the idea that the decision problem is defined as Is there a path P such that the cost is lower than C? and you can easily check this is true by verifying a path you receive. However, what if there is no path that fits this…
wjmccann
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Is finding a weight-balanced tree NP-hard?

In the following, we consider binary trees where only the leaves have weights. Let $T$ be a binary tree and $W(T)$ be the sum of the weights of its leaves. Let $T.l$ and $T.r$ be the left child and right child respectively. We define the imbalance…
rex123
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Algorithm to test whether a language specified in algebraic form is context-free

Is there an algorithm/systematic procedure to test whether a language is context-free? In other words, given a language specified in algebraic form (think of something like $L=\{a^n b^n a^n : n \in \mathbb{N}\}$), test whether the language is…
D.W.
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Why there are no approximation algorithms for SAT and other decision problems?

I have an NP-complete decision problem. Given an instance of the problem, I would like to design an algorithm that outputs YES, if the problem is feasible, and, NO, otherwise. (Of course, if the algorithm is not optimal, it will make errors.) I…
Ribz
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Why are computability problems always written in full caps?

Maybe this is an odd question. It has always bugged me that computability problems are written in all caps, and in such an "awkward" way. SAT, 3-SAT, COLORING, 3-COLORING, PARTITION, CLIQUE, VERTEX COVER. Etc. They're not proper titles, just single…
user162598
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3 answers

Is Deciding Decidability Decidable?

I am wondering if deciding the decidability of problem is a decidable problem. I am guessing not, but after initial searches I cannot find any literature on this problem.
sync
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What is the difference between "Decision" and "Verification" in complexity theory?

In Michael Sipser's Theory of Computation on page 270 he writes: P = the class of languages for which membership can be decided quickly. NP = the class of languages for which membership can be verified quickly. What is the difference between…
BrotherJack
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Test whether two languages are equal, when give in algebraic form

This sub-problem is motivated by Algorithm to test whether a language is regular. Suppose we have two languages $L_1,L_2$ that are expressed in "algebraic" form, as formalized below. I want to determine whether $L_1 = L_2$. Is this decidable? If…
D.W.
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Is there an efficient algorithm for expression equivalence?

e.g. $xy+x+y=x+y(x+1)$ ? The expressions are from ordinary high-school algebra, but restricted to arithmetic addition and multiplication (e.g. $2+2=4; 2.3=6$), with no inverses, subtraction or division. Letters are variables. If it helps, we can…
hyperpallium
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Is there an efficient test for if an NFA accepts a subset of another NFA?

So, I know that testing if a regular language $R$ is a subset of regular language $S$ is decidable, since we can convert them both to DFAs, compute $R \cap \bar{S}$, and then test if this language is empty. However, since this requires converting to…
Joey Eremondi
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Is the equality of two DFAs a decidable problem?

So given two DFAs, is the problem of finding if they generate the same language a Decidable problem? I already know that Equality of two CFL is not Decidable but what about Equality of two DFAs? considering most of the problems with DFAs are…
Richard Jones
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