Galois Connections for Flow Algebras

• Main Authors: Filipiuk, Piotr, Terepeta, Michał, Nielson, Hanne, Nielson, Flemming
• Other Authors: Danmarks Tekniske Universitet = Technical University of Denmark (DTU), Roberto Bruni, Juergen Dingel, TC 6, WG 6.1
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: [INFO]Computer Science [cs]; [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI]; Iceland
• Online Access: https://hal.inria.fr/hal-01583315; https://hal.inria.fr/hal-01583315/document; https://hal.inria.fr/hal-01583315/file/978-3-642-21461-5_9_Chapter.pdf; https://doi.org/10.1007/978-3-642-21461-5_9

International audience We generalise Galois connections from complete lattices to flow algebras. Flow algebras are algebraic structures that are less restrictive than idempotent semirings in that they replace distributivity with monotonicity and dispense with the annihilation property; therefore they are closer to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras using Galois connections such that correctness of the analyses is preserved. The approach is illustrated for a mutual exclusion algorithm.