# Questions tagged [complexity-theory]

Questions related to the (computational) complexity of solving problems

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### Is it NP-hard to fill up bins with minimum moves?

There are $n$ bins and $m$ type of balls. The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$. You start with $b_j$ balls of type $j$. Each ball of ...
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### Why the Cook-Levin reduction is not a parsimonious reduction?

In the textbook Arora-Barak, after presenting the Cook-Levin theorem's proof the authors say that the proof can be modified slightly to make the reduction parsimonious. The parsimonious reduction is ...
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### The relationship between matrix inversion, the HHL algorithm, and the unlikely scenario that $BQP = PSPACE$

I am studying the quantum computing algorithm presented in the paper Quantum algorithm for linear systems of equations}. Without going through all the details, the HHL algorithm is able to apply an ...
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### Reduce factoring to solving quadratic equations

The problem of solving quadratic equations is as follows: Suppose you are given a set of quadratic equations and are asked to find $0$-$1$ values for the variables such that all equations are ...
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### Time complexity of languages recognized by linear bounded automata with restricted number of writes

Suppose that $L$ is a language recognized by a linear-bounded automaton with the constraint that it can only change each of its input cells at most $t$ times each, where $t$ is some constant integer. ...
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### Interactive proofs for coNP languages proof clarification

I was reading a paper by Lance Fortnow and Michael Sipser. "Are there interactive protocols for co-NP languages?" Information Processing Letters 28 v5 (1988), pp. 249-251. An online version of the ...
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### propositional Modal logic filtration definition

Hello I have a slightly unusual question which relates to a definition of filtration structure. The following is my current state of the definition: $\mathcal{M} = (W, R, L)$, W is a set of worlds, ...
Consider the following problem: Let there be a set A of $n$ items $A=\{z_1, ..., z_n\}$, and let $W$ be a strictly positive integer. Each item $z_i$ has a value $v_i$ and a weight $w_i$. Finding a ...