Computer Science – Logic in Computer Science
Scientific paper
2008-09-02
LMCS 4 (3:11) 2008
Computer Science
Logic in Computer Science
A preliminary version of this paper appears in the Proceedings of the 33rd International Colloquium on Automata, Languages and
Scientific paper
10.2168/LMCS-4(3:11)2008
The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched μ-calculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and ExpTime-complete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptiness problems are ExpTime-complete, and then reducing satisfiability in the relevant logics to these problems. The automata models we introduce are two-way graded alternating parity automata over infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched μ-calculus extends the standard μ-calculus.
Bonatti Piero A.
Lutz Carsten
Murano Aniello
Vardi Moshe Y.
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