The paper studies transformations of automata and games using Muller conditions into equivalent ones using parity or Rabin conditions. The authors present two main transformations:
A transformation that turns a deterministic Muller automaton into an equivalent deterministic parity automaton. This transformation is shown to be optimal, in the sense that the resulting parity automaton is minimal amongst those that can be derived from the original automaton by duplication of states.
A transformation that provides an equivalent history-deterministic Rabin automaton from a Muller automaton. This Rabin automaton is also shown to be minimal amongst history-deterministic Rabin automata that can be derived from the original Muller automaton.
The authors introduce the notions of locally bijective morphisms and history-deterministic mappings to formally capture the correctness and optimality of these transformations.
The proposed transformations are based on a novel data structure called the alternating cycle decomposition (ACD), which extends and generalizes the Zielonka tree. The ACD provides a compact representation of the accepting and rejecting cycles of a Muller automaton, capturing the interplay between the structure of the underlying graph and the acceptance condition.
Beyond the transformations, the paper also provides several structural results about Muller transition systems using the ACD, including characterizations for relabelling automata with different acceptance conditions and a comprehensive study of a normal form for parity automata.
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by Anto... lúc arxiv.org 04-23-2024
https://arxiv.org/pdf/2305.04323.pdfYêu cầu sâu hơn