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Capturing Bisimulation-Invariant Complexity Classes with Higher-Order Modal Fixpoint Logic

Abstract : Polyadic Higher-Order Fixpoint Logic (PHFL) is a modal fixpoint logic obtained as the merger of Higher-Order Fixpoint Logic (HFL) and the Polyadic μ-Calculus. Polyadicity enables formulas to make assertions about tuples of states rather than states only. Like HFL, PHFL has the ability to formalise properties using higher-order functions. We consider PHFL in the setting of descriptive complexity theory: its fragment using no functions of higher-order is exactly the Polyadic μ-Calculus, and it is known from Otto’s Theorem that it captures the bisimulation-invariant fragment of PTIME. We extend this and give capturing results for the bisimulation-invariant fragments of EXPTIME, PSPACE, and NLOGSPACE.
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Martin Lange, Etienne Lozes. Capturing Bisimulation-Invariant Complexity Classes with Higher-Order Modal Fixpoint Logic. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. pp.90-103, ⟨10.1007/978-3-662-44602-7_8⟩. ⟨hal-01402031⟩

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