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Questions tagged [minimization]

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13 votes
1 answer
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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 $L(A)=L(B)$? ...
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0 votes
0 answers
38 views

Is it possible to count the total number of local minima for a scalar, multivariate function?

We can assume the function is differentiable, but it is also non-convex and setting the gradient equal to zero has no analytical solution. We can also assume that the domain is bounded, namely the ...
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  • 1
-1 votes
1 answer
88 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 ...
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  • 203
0 votes
1 answer
108 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 ...
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  • 175
4 votes
1 answer
447 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 $L = L(X)$. ...
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2 votes
1 answer
113 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 "...
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9 votes
0 answers
93 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 ...
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  • 414
8 votes
0 answers
140 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 ...
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  • 181
-1 votes
1 answer
64 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 ...
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  • 1
4 votes
1 answer
227 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 ...
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7 votes
1 answer
228 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 ...
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  • 434
0 votes
0 answers
28 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 ...
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  • 471
1 vote
0 answers
145 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 ...
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  • 11
5 votes
1 answer
235 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 ...
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  • 4,331
4 votes
0 answers
833 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 ...
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  • 4,331
9 votes
2 answers
394 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 ...
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1 vote
0 answers
126 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 ...
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1 vote
0 answers
177 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 ...
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0 votes
0 answers
516 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 ...
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14 votes
2 answers
555 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 ...
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  • 9,358
3 votes
0 answers
125 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 ...
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3 votes
0 answers
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 ...
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  • 31
7 votes
2 answers
404 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 ...
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  • 9,358
1 vote
0 answers
641 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 ...
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  • 11
14 votes
1 answer
591 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 ...
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1 vote
0 answers
39 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 ...
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4 votes
3 answers
591 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 ...
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