Pumping Lemma for Infinite Alphabets
Analysis
This paper addresses a fundamental question in theoretical computer science: how to characterize the structure of languages accepted by certain types of automata, specifically those operating over infinite alphabets. The pumping lemma is a crucial tool for proving that a language is not regular. This work extends this concept to a more complex model (one-register alternating finite-memory automata), providing a new tool for analyzing the complexity of languages in this setting. The result that the set of word lengths is semi-linear is significant because it provides a structural constraint on the possible languages.
Key Takeaways
- •Extends the pumping lemma to languages over infinite alphabets.
- •Focuses on languages accepted by one-register alternating finite-memory automata.
- •Shows that the set of word lengths in such languages is semi-linear.
Reference
“The paper proves a pumping-like lemma for languages accepted by one-register alternating finite-memory automata.”