LTL to self-loop alternating automata with generic acceptance and back

Abstract Self-loop alternating automata (SLAA) with Buchi or co-Buchi acceptance are popular formalisms also known as very weak alternating automata (VWAA). They are often used as an intermediate results in translations of LTL to deterministic or nondeterministic automata. This paper considers SLAA with generic transition-based Emerson-Lei acceptance and presents translations of LTL to these automata and back. Importantly, the translation of LTL to SLAA with generic acceptance produces considerably smaller automata than previous translations of LTL to Buchi or co-Buchi SLAA. Our translation is already implemented in the tool ltl3tela, where it helps to produce small deterministic or nondeterministic transition-based Emerson-Lei automata for given LTL formulae.