The Descriptive Complexity of the Deterministic Exponential Time Hierarchy

Freire, Cibele; Martins, Ana Teresa

doi:10.1016/j.entcs.2011.03.006

Cited by 1 publication

(4 citation statements)

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“…Here we can only state that it is possible to capture these in terms of natural fragments of PHFL as well but the proof requires a few more ingredients than the time-complexity case. Here we could use the already known characterisation of k-EXPTIME by Higher-Order Predicate Logics with Least Fixpoints [6]. For the space complexity classes, we need to first develop such characterisations that extend the Abiteboul-Vianu Theorem.…”

Section: Discussionmentioning

confidence: 99%

“…We introduce Higher-Order Logic with Least Fixpoints (HO(LFP)) to make use of the characterisation of k-EXPTIME over the class of ordered structures as the queries definable in order-(k + 1) HO(LFP), due to Immerman and Vardi [8,20,9], resp. Freire and Martins [6].…”

Section: Higher-order Logic With Least Fixpointsmentioning

confidence: 99%

“…4 we prepare for the more difficult and other half of the capturing result. We rely on a logical characterisation of k-EXPTIME in terms of Higher-Order Predicate Logic with Fixpoints [6], and a key step in expressing such (bisimulation-invariant) queries in Higher-Order Modal Fixpoint is the modelling of higher-order quantification using an enumeration technique. In Sect.…”

Section: Introductionmentioning

confidence: 99%

“…first-order logic with least fixpoints. It's generalisation is the following: 8,20,9,6]). For each k ≥ 0, HO k+1 (LFP) captures k-EXPTIME over the class of ordered structures.…”

mentioning

confidence: 99%

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Capturing Bisimulation-Invariant Exponential-Time Complexity Classes

Bruse

Kronenberger

Lange

2022

Electron. Proc. Theor. Comput. Sci.

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Otto's Theorem characterises the bisimulation-invariant PTIME queries over graphs as exactly those that can be formulated in the polyadic µ-calculus, hinging on the Immerman-Vardi Theorem which characterises PTIME (over ordered structures) by First-Order Logic with least fixpoints. This connection has been extended to characterise bisimulation-invariant EXPTIME by an extension of the polyadic µ-calculus with functions on predicates, making use of Immerman's characterisation of EXPTIME by Second-Order Logic with least fixpoints.In this paper we show that the bisimulation-invariant versions of all classes in the exponential time hierarchy have logical counterparts which arise as extensions of the polyadic µ-calculus by higher-order functions. This makes use of the characterisation of k-EXPTIME by Higher-Order Logic (of order k + 1) with least fixpoints, due to Freire and Martins.

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Section: Discussionmentioning

confidence: 99%

Section: Higher-order Logic With Least Fixpointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…first-order logic with least fixpoints. It's generalisation is the following: 8,20,9,6]). For each k ≥ 0, HO k+1 (LFP) captures k-EXPTIME over the class of ordered structures.…”

mentioning

confidence: 99%

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