Questions tagged [minimization]

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14
votes
2answers
481 views

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 ...
12
votes
1answer
425 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 ...
9
votes
2answers
275 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 ...
7
votes
1answer
185 views

Finding a minimal DFA whose language has a desired intersection with another

Suppose I have regular languages $B \subseteq A$, with corresponding (known) minimal deterministic finite automata $M_A, M_B$. I would like to find another regular language $C$ such that $B = A \cap ...
7
votes
2answers
191 views

A tool for minimal NFA computation

It is well known that minimizing an NFA for a fixed regular language is $PSPACE-Complete$. As far as I know, there are no better than trivial algorithms for minimizing such NFA, but there's a little ...
5
votes
1answer
210 views

Minimizing a submodular function given noisy oracle access

Let $f\colon 2^{[n]} \to \mathbb{R}$ be a submodular function (one can assume $f$ is bounded, if this helps). We are given noisy oracle access to $f$: on any $S$ and for any $\tau > 0$, one can ...
4
votes
3answers
417 views

How to minimize a FSM transducer?

In contrast to FSM minimization which is well studied with various algorithms, theorems and has many practical applications, I'm looking for any nontrivial insight, analysis and references to the ...
4
votes
1answer
125 views

Is there an algorithm for minimizing an NFA with respect to bisimilarity rather than language equivalence?

DFA minimization is the problem of transforming a given automaton to an equivalent one with the minimum number of states. Equivalence is taken to be language equivalence. Milner introduced the notion ...
3
votes
0answers
461 views

Minimizing a monotone submodular function under a cardinality constraint

I would like to know what the status of the following question is: Given query access to a non-decreasing, non-negative submodular function $f\colon 2^{[n]} \to \mathbb{R}$ and a parameter $0 \leq ...
3
votes
0answers
110 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 ...
3
votes
0answers
849 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 ...
2
votes
0answers
439 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 ...
1
vote
0answers
123 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 ...
1
vote
0answers
117 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 ...
1
vote
0answers
126 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 ...
1
vote
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 ...
0
votes
0answers
25 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 ...
0
votes
0answers
418 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 ...