Conceitos Básicos
History-deterministic Parikh automata (HDPA) represent a new class of languages, offering a balance between expressiveness and computational feasibility by restricting nondeterminism in Parikh automata.
Resumo
Bibliographic Information: Erlich, E., Grobler, M., Guha, S., Jecker, I., Lehtinen, K., & Zimmermann, M. (2024). History-deterministic Parikh Automata. arXiv preprint arXiv:2209.07745v3.
Research Objective: This paper investigates the expressiveness, closure properties, and algorithmic aspects of history-deterministic Parikh automata (HDPA), a novel class of automata that bridges the gap between deterministic and nondeterministic Parikh automata.
Methodology: The authors introduce the formal definition of HDPA, establish a pumping lemma for this class, and compare their expressiveness with other related automata models, including deterministic and nondeterministic Parikh automata, unambiguous Parikh automata (UCA and WUPA), and reversal-bounded counter machines. They further analyze the closure properties of HDPA under various operations and explore the decidability and complexity of decision problems related to HDPA.
Key Findings:
HDPA are strictly more expressive than deterministic Parikh automata (DPA) but less expressive than nondeterministic Parikh automata (PA).
HDPA are incomparable in expressiveness to both UCA and WUPA.
HDPA possess almost all closure properties of DPA, except for complementation.
Safety model checking for HDPA is decidable, while universality, inclusion, equivalence, and regularity are undecidable.
Determining whether a Parikh automaton is history-deterministic or equivalent to an HDPA is undecidable.
Main Conclusions: HDPA constitute a distinct class of languages capable of capturing quantitative features. They offer a compromise between the expressiveness of PA and the desirable algorithmic properties of DPA. However, certain decision problems, such as determining history-determinism or equivalence to an HDPA, remain undecidable.
Significance: This research contributes to the field of automata theory by introducing and analyzing a new class of automata with restricted nondeterminism. The findings have implications for areas such as model checking and quantitative verification.
Limitations and Future Research: The paper primarily focuses on HDPA over finite words. Exploring HDPA over infinite words and further investigating the complexity of resolving nondeterminism in HDPA are potential avenues for future research.