Alternating automata on infinite trees
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
Determinization and memoryless winning strategies
Information and Computation
Languages, automata, and logic
Handbook of formal languages, vol. 3
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Efficent Local Model-Checking for Fragments of teh Modal µ-Calculus
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
On the undecidability of logics with converse, nominals, recursion and counting
Artificial Intelligence
Reasoning in expressive description logics with fixpoints based on automata on infinite trees
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Enriched µ-calculi module checking
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Enriched µ-calculus pushdown module checking
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
SPARQL query containment under RDFS entailment regime
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Pushdown module checking with imperfect information
Information and Computation
A Goal-Directed Decision Procedure for Hybrid PDL
Journal of Automated Reasoning
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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 this problem. The automata models we introduce are two-way graded alternating parity automata over infinite trees (2GAPT) and fully enriched automata (FEA) 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