LNAI 2842 Identification with Probability One of Stochastic Deterministic Linear Languages 1st Edition by Colin de la Higuera, Jose Oncina ISBN 9783540200574 354020057X

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ISBN 10: 354020057X
ISBN 13: 9783540200574
Author: Colin de la Higuera, Jose Oncina

Learning context-free grammars is generally considered a very hard task. This is even more the case when learning has to be done from positive examples only. In this context one possibility is to learn stochastic context-free grammars, by making the implicit assumption that the distribution of the examples is given by such an object. Nevertheless this is still a hard task for which no algorithm is known. We use recent results to introduce a proper subclass of linear grammars, called deterministic linear grammars, for which we prove that a small canonical form can be found. This has been a successful condition for a learning algorithm to be possible. We propose an algorithm for this class of grammars and we prove that our algorithm works in polynomial time, and structurally converges to the target in the paradigm of identification in the limit with probability 1. Although this does not ensure that only a polynomial size sample is necessary for learning to be possible, we argue that the criterion means that no added (hidden) bias is present.

LNAI 2842 Identification with Probability One of Stochastic Deterministic Linear Languages 1st Edition Table of contents:

Chapter 1: Introduction to Language Identification

• Definition and Importance of Language Identification
• Types of Formal Languages: Deterministic, Stochastic, and Linear Languages
• Historical Background and Key Developments in Language Learning Theory
• The Role of Probability in Language Learning

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Chapter 2: Stochastic and Deterministic Languages

• Defining Stochastic Deterministic Linear Languages
• Comparison with Other Types of Formal Languages
• Properties of Stochastic and Deterministic Languages
• Examples of Stochastic Deterministic Linear Languages
• The Role of Probability in Stochastic Languages

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Chapter 3: The Theory of Identification with Probability One

• The Concept of Identification with Probability One (IP1)
• Algorithms for Identification with Probability One
• Importance of Identifying Languages with Probability One in Computational Learning
• The Role of Stochastic Models in Language Identification

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Chapter 4: Linear Languages and Their Properties

• Introduction to Linear Languages
• The Structure and Syntax of Linear Languages
• Stochastic Deterministic Linear Languages: Specific Properties
• Parsing and Processing Linear Languages
• The Role of Linear Languages in Formal Language Theory

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Chapter 5: Algorithmic Approach to Language Identification

• Overview of Algorithmic Techniques for Language Identification
• Stochastic Models and Deterministic Algorithms
• Proposed Algorithms for Identifying Stochastic Deterministic Linear Languages
• Efficiency and Complexity of Language Identification Algorithms
• Case Studies and Experimental Results

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Chapter 6: Probabilistic Models in Language Learning

• The Role of Probability in Language Modeling
• Techniques for Incorporating Probability in Language Identification
• Modeling Uncertainty in Stochastic Deterministic Languages
• Use of Probabilistic Grammars in Language Learning

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Chapter 7: Identification with Probability One in Stochastic Deterministic Linear Languages

• Detailed Algorithm for Identifying Stochastic Deterministic Linear Languages with Probability One
• Theoretical Foundations of the Algorithm
• Practical Application and Implementation of the Algorithm
• Examples and Step-by-Step Explanations
• Analysis of Results and Performance

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Chapter 8: Theoretical Implications and Insights

• Theoretical Analysis of the Language Identification Process
• Contributions to the Field of Formal Language Theory
• The Relationship Between Stochastic Models and Language Learning
• Implications for Computational Linguistics and Machine Learning

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Chapter 9: Applications and Future Directions

• Real-World Applications of Stochastic Deterministic Linear Languages
• Potential Use Cases in Computational Linguistics and AI
• Improving the Efficiency of Language Identification Algorithms
• Directions for Future Research in Language Learning and Formal Grammars

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Conclusion

• Summary of Key Findings
• Final Thoughts on Identification with Probability One
• Contributions to Formal Language Theory and Algorithmic Learning

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Appendices

• Appendix A: Detailed Algorithmic Code and Pseudocode
• Appendix B: Glossary of Terms and Notations
• Appendix C: Further Reading and Resources on Formal Language Theory
• Appendix D: Additional Case Studies and Examples

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Index

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