Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Optimality in Abstractions of Model Checking
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Specification and verification of concurrent systems in CESAR
Proceedings of the 5th Colloquium on International Symposium on Programming
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Automatic Abstraction Using Generalized Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
Three-Valued Abstractions of Games: Uncertainty, but with Precision
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Model Checking Vs. Generalized Model Checking: Semantic Minimizations for Temporal Logics
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
3-Valued Abstraction: More Precision at Less Cost
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Systematic construction of abstractions for model-checking
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Ranked predicate abstraction for branching time: complete, incremental, and precise
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
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We define, for any partition of a state space and for formulas of the modal µ-calculus, two variants of precision for abstractions that have that partition set as state space. These variants are defined via satisfaction parity games in which the Refuter can replace a concrete state with any state in the same partition before, respectively after, a quantifier move. These games are independent of the kind of abstraction. Our first variant makes the abstraction games of de Alfaro et al. model-independent, captures the definition of precision given by Shoham & Grumberg, and corresponds to generalized Kripke modal transition systems. Our second variant is then shown, for a fixed abstraction function, to render more precise abstractions through µ-automata without fairness.We discuss tradeoffs of both variants in terms of the size of abstractions, the perceived cost of their synthesis via theorem provers, and the preservation of equations that are valid over concrete models. Finally, we sketch a combination of both abstraction methods.