The 2024 Developer Survey results are live! See the results

# Questions tagged [minimization]

The tag has no usage guidance.

29 questions
Filter by
Sorted by
Tagged with
37 views

### Applying $/mu$-Operator for Unbounded minimization

I'm learning how to use the $\mu$-Operator for unbounded minimization and trying to define a partial recursive function $g(y,z)$ from the primitive recursive function $f$ defined as:  f(x, y, z) = ...
88 views

### Minimizing a submodular function containing summation and production under partition matroid constraint

I'm having difficulty solving the following problem: We're given $n$ sets $X_1,\ldots, X_n$. Each set $X_i=\{(a_i,b_i)\}$ contains poly(n) many ordered pairs of non-negatives with $0\le a_i+b_i\le 1$. ...
• 483
1 vote
285 views

### Graph partitioning to minimize sum of intra-partition edge weights

I've seen a lot of graph partitioning algorithms w/ the objective of minimizing the weight of inter-partition edges, (e.g. k-way partitioning) but haven't quite found anything on minimizing the total ...
• 11
530 views

### Complexity of NFA to DFA minimization with binary threshold

What is the complexity of the following problem? Given an NFA $A$ and a number $k\in \mathbb{N}$ in binary encoding, does there exist a DFA $B$ with at most $k$ states such that $L(A)=L(B)$? ...
• 5,596
89 views

### Is finding the shortest consistent term to fill a missing line in a truth table still NP-hard?

I understand the logic minimization problem is NP-hard when given the onset, since the last step is equivalent to set cover optimization. If instead we are given a partial truth table, and we just ...
• 203
234 views

### Epsilon-closure and DFA minimization algorithms for probabilistic NFA

Are there any algorithms performing e-closures and DFA minimizations for probabilistic Finite Automata? Given that probabilistic NFAs might have multiple accepting paths for generating equivalent ...
• 175
767 views

### Can we efficiently convert from NFA to smallest equivalent DFA?

Definitions For any automaton $X$, let $L(X)$ denote the language recognized by $X$. For any language $L$, let $sc(L)$ denote the number of states in the smallest DFA $X$ such that $L = L(X)$. ...
• 5,147
199 views

### NP-Completeness of Finding Minimum Automaton, in Gold's paper

I have been investigating "learning automatas", and I came across reference to Gold's papers several times: "Complexity Of Automaton Identification From Given Data", and "...
• 146
129 views

### Reference request: DFA linear-time minimization

What is the most complicated kind of deterministic finite-state automaton that can be minimized in $O(n)$ time? Here’s what I’ve been able to find so far: The acyclic case has been solved. So any ...
• 434
159 views

### Determining if transducer automaton has two states with intersecting images, without minimizing?

I work (in implementation!) with deterministic finite state automata with input and output; i.e. there are transitions (start state,input letter)$\to$(new state,output letter). Thus every state gives ...
• 191
85 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 ...
• 1
289 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 ...
259 views

• 4,481
497 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 ...
• 2,252
1 vote
128 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
226 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
611 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 ...
603 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 ...
• 9,478
132 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 ...
• 11.1k
1k 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 ...
• 31
506 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 ...
• 9,478
1 vote
770 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 ...
• 11
646 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 ...
• 10.3k
1 vote
40 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 ...
• 174