# Questions tagged [minimization]

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### Does XOR automata (NXA) for finite languages benefit from cycles?

A non-deterministic Xor automata (NXA) is syntactically an NFA, but a word is said to be accepted by NXA if it has an odd number of accepting paths (instead of at least one accepting path in the NFA ...
1answer
444 views

### Minimizing residual finite state automata

Residual finite state automata (RFSAs, defined in [DLT02]) are NFAs that have some nice features in common with DFAs. In particular, there is always a canonical minimum sized RFSA for every regular ...
2answers
291 views

### Generalizing Brzozowski's DFA minimization algorithm to finite automata with different classes of accepting states?

Brzozowski's algorithm for converting a DFA into an equivalent minimum-state DFA is remarkably simple: if $R(D)$ denotes the NFA formed by reversing all the edges in a DFA $D$, making the old start ...
1answer
202 views

0answers
111 views

### minimal languages that “cover” grammar productions

this question is based on generalizing two somewhat similar questions that recently appeared on the "sister" beta site cs.se (now with more questions than this one!) and which seems theoretically ...
0answers
890 views

### Christofides algorithm for directed graph

Is it possible to implement the Christofides algorithm for an directed Graph? Suppose you have an undirected Graph, in which every vertex has an edges in both ways to every other in the graph (not to ...
0answers
460 views

### Splitting a graph into size constrained clusters

I ran across a problem while working on an algorithm for a game I'm making on the side. It's basically a clustering problem where we have a graph G and want to split it into clusters of equal size ...
0answers
132 views

### QUBO formulation of a discrete-variable optimization problem

I am facing a non-linear, discrete optimization problem, which I can formulate in this abstract manner: I have a certain non-analytic non-linear real-valued function $f:S \to \mathbb{R}$ which takes ...
0answers
119 views

### Minimize L2 norm by circular permutation

Imagine two lists $L$, $M$ of the same length $n$. How to find $j$ such that $\sum_{i=1}^n(L[i]-M[i+j])^2$ is minimal, where the index $i+j$ is taken modulo $n$? Of course one can take all the ...
0answers
139 views

### 3D Bin Packing with one bin with infinite/unknown size

Hi I'm looking for a variation of the Orthogonal 3D-BinPacking algorithm with only one bin of unknown size. I have a set $S$ of $n$ cuboids items $i_j$ with $j=1...n$. The dimensions of the items are ...
0answers
38 views

### Determine whether a categorical grammar is minimal concerning lexical entries

In order to compare the descriptional complexity of context-free and (combinatoric) categorical I need a way to check if a categorical grammar of a formal language is minimal concerning lexical ...
0answers
26 views

### Searchable finite field

Let $F$ be a large finite field, where the elements are strings of length $n$. We require, addition, multiplication, and division to be efficient (polynomial in $n$). We say that $F$ is searchable if ...
0answers
443 views

### Hardness of Minimizing Submodular Functions with Cardinality Constraints

I am new to submodular functions and I am reading the introductions to submodular functions and applications ( https://www.ima.umn.edu/optimization/seminar/queyranne.pdf ). In this introduction, it ...
1answer
52 views

### How to find for each 3-input boolean function the minimum number of NAND operators needed to compute it [closed]

I need to know for each of the $2^{2^3}$ boolean functions with $3$ inputs the smallest boolean circuit made only of NAND gates computing it (smallest in terms of the number gates). I would be glad ...