Eliminating ε-Transitions in Weighted Automata: Difference between revisions

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Created page with "Title: Eliminating ε-Transitions in Weighted Automata Abstract: This research focuses on weighted automata with ε-transitions, a particular type of automaton that models various applications like image compression, speech recognition, and probabilistic modeling. The main goal is to develop an algebraic method to eliminate ε-transitions and convert the automaton into an equivalent one without ε-transitions, while maintaining the same behavior. This method is based on..."
 
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Title: Eliminating ε-Transitions in Weighted Automata
Title: Eliminating ε-Transitions in Weighted Automata


Abstract: This research focuses on weighted automata with ε-transitions, a particular type of automaton that models various applications like image compression, speech recognition, and probabilistic modeling. The main goal is to develop an algebraic method to eliminate ε-transitions and convert the automaton into an equivalent one without ε-transitions, while maintaining the same behavior. This method is based on the concept of a semiring, which is a set with two operations and their neutral elements, and the star of matrices, which represents the inverse of a matrix. The running time complexity of the method is deduced from that of matrix multiplication, making it efficient for well-known semirings like boolean and tropical. The paper concludes with a discussion on the equivalence between the two types of automata and the validity of the method.
Abstract:
This research focuses on the elimination of ε-transitions in weighted automata, a type of automaton used to model various purposes such as image compression, speech recognition, and formal linguistic. The study presents an algebraic method to compute the star of transition matrices for ε, which is used to eliminate ε-transitions and preserve the automaton's behavior. The running time complexity of the method is discussed, and it is shown to be efficient for well-known semirings like boolean and tropical. The paper concludes with a discussion on the equivalence between k-automata and k-ε-automata, and the validity of the method.


Main Research Question: Can we develop an efficient method to eliminate ε-transitions in weighted automata while maintaining the same behavior?
Main Research Question:
Can we develop an efficient method to eliminate ε-transitions in weighted automata while preserving the automaton's behavior?


Methodology: The methodology involves the following steps:
Methodology:
The study uses the concept of semirings, which are sets with two laws and their neutrals. The paper introduces the notions of k-automaton and k-ε-automaton, and presents the main results: a method to eliminate ε-transitions and an algorithm to suppress them while preserving the behavior. The method's running time complexity is discussed, and it is shown to be efficient for well-known semirings.


1. Defining a semiring, which is a set with two operations (⊕, ⊗) and their neutral elements (0, 1).
Results:
2. Introducing the concept of a star of a scalar, which represents the inverse of a matrix.
The research presents an algebraic method to compute the star of transition matrices for ε, which is used to eliminate ε-transitions and preserve the automaton's behavior. The method's running time complexity is discussed, and it is shown to be efficient for well-known semirings like boolean and tropical.
3. Defining a weighted automaton and a weighted ε-automaton, which are models used to represent weighted systems with multiplicities and ε-transitions, respectively.
4. Developing an algebraic method to eliminate ε-transitions by finding the star of matrices and converting the weighted ε-automaton into an equivalent weighted automaton without ε-transitions.


Results: The main result is an algebraic method to eliminate ε-transitions in weighted automata. The method is based on the concept of a semiring and the star of matrices, and it ensures that the converted automaton behaves similarly to the original one. The running time complexity of the method is deduced from that of matrix multiplication, making it efficient for well-known semirings like boolean and tropical.
Implications:
The results of this research have implications in various fields such as image compression, speech recognition, formal linguistic, and probabilistic modeling. The ability to eliminate ε-transitions in weighted automata can lead to more efficient and accurate models, and the developed method can be applied to a wide range of problems.


Implications: The elimination of ε-transitions in weighted automata has several implications:
Keywords:
Weighted Automata, ε-Transitions, Behavior, Star of Matrices, Semirings, Algebraic Method, Running Time Complexity


1. Simplifying the automaton, making it easier to analyze and understand.
Link to Article: https://arxiv.org/abs/0401012v2
2. Enabling the use of existing algorithms and tools designed for weighted automata without ε-transitions.
3. Providing a more efficient way to model weighted systems with multiplicities and ε-transitions, which can lead to better performance in applications like image compression, speech recognition, and probabilistic modeling.
 
Conclusion: In conclusion, this research has developed an efficient method to eliminate ε-transitions in weighted automata while maintaining the same behavior. The method is based on the concept of a semiring and the star of matrices, and it has several implications for the modeling and analysis of weighted systems with multiplicities and ε-transitions.
 
Link to Article: https://arxiv.org/abs/0401012v1
Authors:  
Authors:  
arXiv ID: 0401012v1
arXiv ID: 0401012v2


[[Category:Computer Science]]
[[Category:Computer Science]]
[[Category:Ε]]
[[Category:Ε]]
[[Category:Method]]
[[Category:Transitions]]
[[Category:Transitions]]
[[Category:Weighted]]
[[Category:Method]]
[[Category:Automata]]
[[Category:Automata]]
[[Category:Automaton]]

Latest revision as of 15:13, 24 December 2023

Title: Eliminating ε-Transitions in Weighted Automata

Abstract: This research focuses on the elimination of ε-transitions in weighted automata, a type of automaton used to model various purposes such as image compression, speech recognition, and formal linguistic. The study presents an algebraic method to compute the star of transition matrices for ε, which is used to eliminate ε-transitions and preserve the automaton's behavior. The running time complexity of the method is discussed, and it is shown to be efficient for well-known semirings like boolean and tropical. The paper concludes with a discussion on the equivalence between k-automata and k-ε-automata, and the validity of the method.

Main Research Question: Can we develop an efficient method to eliminate ε-transitions in weighted automata while preserving the automaton's behavior?

Methodology: The study uses the concept of semirings, which are sets with two laws and their neutrals. The paper introduces the notions of k-automaton and k-ε-automaton, and presents the main results: a method to eliminate ε-transitions and an algorithm to suppress them while preserving the behavior. The method's running time complexity is discussed, and it is shown to be efficient for well-known semirings.

Results: The research presents an algebraic method to compute the star of transition matrices for ε, which is used to eliminate ε-transitions and preserve the automaton's behavior. The method's running time complexity is discussed, and it is shown to be efficient for well-known semirings like boolean and tropical.

Implications: The results of this research have implications in various fields such as image compression, speech recognition, formal linguistic, and probabilistic modeling. The ability to eliminate ε-transitions in weighted automata can lead to more efficient and accurate models, and the developed method can be applied to a wide range of problems.

Keywords: Weighted Automata, ε-Transitions, Behavior, Star of Matrices, Semirings, Algebraic Method, Running Time Complexity

Link to Article: https://arxiv.org/abs/0401012v2 Authors: arXiv ID: 0401012v2

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