Editing 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.

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

Methodology: The methodology involves the following steps:

1. Defining a semiring, which is a set with two operations (⊕, ⊗) and their neutral elements (0, 1).
2. Introducing the concept of a star of a scalar, which represents the inverse of a matrix.
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 elimination of ε-transitions in weighted automata has several implications:

1. Simplifying the automaton, making it easier to analyze and understand.
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: 
arXiv ID: 0401012v1

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