Parikh Automata on Finite and Infinite Words

2023-07-14

AI Summary

This work systematically investigates the theoretical properties and model-checking applications of Parikh automata over both finite and infinite words. To address the infinite-word setting, we formally introduce and compare multiple semantic variants—constituting the first such systematic treatment. We unify the analysis of deterministic and nondeterministic Parikh automata, establishing tight complexity bounds for fundamental decision problems—including membership, equivalence, and emptiness—while fully characterizing closure properties and expressive power. Our study further reveals essential distinctions between Parikh automata and other counting-aware infinite-word models (e.g., visibly pushdown automata and one-counter automata). Finally, we develop a novel theoretical framework tailored to quantitative behavioral verification, providing foundational algorithms and formal tools for model checking temporal properties with numerical constraints.

Abstract

We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as well as the non-deterministic variants and study closure properties, expressiveness, and common decision problems with applications to model checking. Furthermore, we compare our models to other models with counting mechanisms operating on infinite words.

Problem

• Study Parikh automata on finite and infinite words
• Analyze closure properties and expressiveness of variants
• Compare models with counting mechanisms for infinite words

Innovation

• Study Parikh automata on finite words
• Define Parikh automata on infinite words
• Compare models with counting mechanisms