# Difference between revisions of "Publications/casares.22.tacas"

## Abstract

In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., ${\displaystyle \omega }$-automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for ${\displaystyle \omega }$-automata.

## Bibtex (lrde.bib)

@InProceedings{	  casares.22.tacas,
author	= {Antonio Casares and Alexandre Duret-Lutz and Klara J.
Meyer and Florian Renkin and Salomon Sickert},
title		= {Practical Applications of the {A}lternating {C}ycle
{D}ecomposition},
booktitle	= {Proceedings of the 28th International Conference on Tools
and Algorithms for the Construction and Analysis of
Systems},
year		= {2022},
series	= {Lecture Notes in Computer Science},
volume	= {13244},
month		= apr,
abstract	= {In 2021, Casares, Colcombet, and Fijalkow introduced the
Alternating Cycle Decomposition (ACD) to study properties
and transformations of Muller automata. We present the
first practical implementation of the ACD in two different
tools, Owl and Spot, and adapt it to the framework of
Emerson-Lei automata, i.e., $\omega$-automata whose
acceptance conditions are defined by Boolean formulas. The
ACD provides a transformation of Emerson-Lei automata into
parity automata with strong optimality guarantees: the
resulting parity automaton is minimal among those automata
that can be obtained by duplication of states. Our
empirical results show that this transformation is usable
in practice. Further, we show how the ACD can generalize
many other specialized constructions such as deciding
typeness of automata and degeneralization of generalized
B{\"u}chi automata, providing a framework of practical
algorithms for $\omega$-automata.},
pages		= {99--117},
doi		= {10.1007/978-3-030-99527-0_6}
}