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About this paper
Anupam Das, Abhishek De
This paper from the University of Birmingham introduces an algebraic theory for ω-regular languages by developing right-linear lattice (RLL) expressions as a notation for alternating parity automata. The work provides a sound and complete axiomatization for the equational theory of these expressions, establishing a connection to the linear-time μ-calculus.
Key insights
- Right-linear lattice (RLL) expressions extend existing right-linear algebras by dualizing syntax to incorporate both union (join) and intersection (meet) operations, along with least (μ) and greatest (ν) fixed-point operators.
- The completeness of the RLL axiomatization is established by leveraging the known completeness of the linear-time μ-calculus (μLTL) through defined translations between RLL expressions and μLTL formulas.
- A game-theoretic mechanism, the Evaluation Game, is provided to decide word membership in languages defined by RLL expressions, reinforcing their connection to alternating parity automata.
Summary by alphaXiv.
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