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Abstract LetGbe a linear real reductive Lie group. Orbital integrals define traces on the group algebra ofG. We introduce a construction of higher orbital integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra ofG. We analyze these higher orbital integrals via Fourier transform by expressing them as integrals on the tempered dual ofG. We obtain explicit formulas for the pairing between the higher orbital integrals and theK-theory of the reduced group$$C^{*}$$-algebra, and we discuss their application toK-theory.
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Checking δ-Satisfiability of Reals with Integrals
Many synthesis and verification problems can be reduced to determining the truth of formulas over the real numbers. These formulas often involve constraints with integrals in them. To this end, we extend the framework of δ-decision procedures with techniques for handling integrals of user-specified real functions. We implement this decision procedure in the tool ∫dReal, which is built on top of dReal. We evaluate ∫dReal on a suite of problems that include formulas verifying the fairness of algorithms and the privacy and the utility of privacy mechanisms and formulas that synthesize parameters for the desired utility of privacy mechanisms. The performance of the tool in these experiments demonstrates the effectiveness of ∫dReal.
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- PAR ID:
- 10642031
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 9
- Issue:
- OOPSLA1
- ISSN:
- 2475-1421
- Format(s):
- Medium: X Size: p. 704-729
- Size(s):
- p. 704-729
- Sponsoring Org:
- National Science Foundation
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