Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages

Core Concepts

Deterministic omega automata that are isomorphic to their right congruence automata, the fully informative classes, can be efficiently learned from polynomial-size characteristic samples.

Abstract

The paper addresses the question of which omega automata have characteristic sets of polynomial size, and whether these sets can be constructed in polynomial time. The key insights are: Non-deterministic omega automata of any common type (Büchi, co-Büchi, parity, Rabin, Streett, Muller) do not have characteristic samples of polynomial size. For deterministic omega automata that are isomorphic to their right congruence automata, the fully informative classes, polynomial time algorithms are provided for constructing characteristic samples and learning from them. The algorithms for constructing characteristic sets in polynomial time require polynomial-time algorithms for (1) equivalence of the respective omega automata, and (2) testing membership of the language of the automaton in the informative classes, which are also provided. The fully informative classes (IBA, ICA, IPA, IRA, ISA, IMA) can be identified in the limit using polynomial time and data. A teacher can construct a characteristic sample not only given an acceptor which is isomorphic to the right congruence of the language, but also given an acceptor which is equivalent to such an acceptor.

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Key Insights Distilled From

Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages

by Dana Angluin... at arxiv.org 04-23-2024

https://arxiv.org/pdf/2209.09336.pdf

Deeper Inquiries

What are the implications of the results in this paper for practical applications of automata learning in formal methods and system design

The results presented in this paper have significant implications for practical applications of automata learning in formal methods and system design. By establishing the existence of characteristic samples for certain classes of omega-regular languages, the paper provides a framework for efficient learning algorithms in the context of grammatical inference. This has direct implications for tasks such as system verification, synthesis, and model learning in various domains. One key implication is the potential for improving the efficiency and accuracy of verification and synthesis algorithms by leveraging the insights from automata learning. By being able to construct concise characteristic samples for specific classes of omega automata, practitioners can streamline the process of inferring models from data, leading to more effective system design and verification processes. Moreover, the development of polynomial-time algorithms for constructing characteristic samples and learning from them opens up new possibilities for automation in formal methods. This can lead to advancements in areas such as program analysis, protocol verification, and software synthesis, where automata-based techniques play a crucial role. Overall, the results of this paper pave the way for the integration of machine learning techniques, specifically automata learning, into formal methods and system design practices, enhancing the capabilities and efficiency of these processes.

Are there any other subclasses of omega-regular languages beyond the fully informative classes that can be efficiently learned from polynomial-size characteristic samples

While the fully informative classes of omega-regular languages discussed in the paper offer efficient learning from polynomial-size characteristic samples, there may be other subclasses that can also be learned efficiently. One potential direction for exploring additional subclasses is to investigate variations or extensions of the fully informative classes that exhibit similar properties conducive to efficient learning. For example, researchers could explore subclasses that have specific structural constraints or properties that enable the construction of concise characteristic samples. By identifying and defining new subclasses based on different criteria or acceptance conditions, it may be possible to discover additional classes of omega-regular languages that are efficiently learnable from polynomial-size characteristic samples. Furthermore, considering variations in the acceptance conditions, such as combining multiple acceptance conditions or introducing novel criteria for accepting words in omega-regular languages, could lead to the identification of new subclasses with efficient learnability properties. By expanding the scope of investigation beyond the fully informative classes, researchers may uncover novel insights into the learnability of omega-regular languages and enhance the applicability of automata learning in various domains.

How do the techniques developed in this paper relate to or build upon prior work on learning omega automata and regular languages in general

The techniques developed in this paper represent a significant advancement in the field of learning omega automata and regular languages, building upon prior work in several key ways. Efficient Teachability and Learnability: The paper introduces the concept of efficient teachability and learnability for omega-regular languages, demonstrating the existence of polynomial-time algorithms for constructing characteristic samples and learning from them. This extends the traditional notions of identifiability in the limit to polynomial time and data, enhancing the practical applicability of automata learning techniques. Fully Informative Classes: By focusing on the fully informative classes of omega automata, the paper establishes a framework for efficient learning from polynomial-size characteristic samples. This contributes to a deeper understanding of the classes of regular ω-languages that can be effectively learned using automata learning techniques. Concise Characteristic Samples: The development of concise characteristic samples for specific subclasses of omega-regular languages highlights the importance of constructing compact and informative samples for efficient learning. This approach builds upon prior work on characteristic samples and extends it to the domain of omega automata. Overall, the techniques and results presented in this paper represent a significant advancement in the field of automata learning, providing new insights and methodologies for efficient learning of omega-regular languages. These contributions build upon and extend prior research in the area, paving the way for enhanced applications of automata learning in formal methods and system design.