Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient generation of counterexamples and witnesses in symbolic model checking
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Tree-Like Counterexamples in Model Checking
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Efficient Diagnostic Generation for Boolean Equation Systems
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
On the Complexity of Parity Word Automata
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Evidence-based verification
Complexity of DNF minimization and isomorphism testing for monotone formulas
Information and Computation
A sub-quadratic algorithm for conjunctive and disjunctive boolean equation systems
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Equivalence checking for infinite systems using parameterized Boolean equation systems
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
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Parameterised Boolean equation systems (PBESs) can be used for solving a variety of verification problems such as model checking and equivalence checking problems. The definition of solution for a PBES is notoriously difficult to understand, which makes them hard to work with. Tan and Cleaveland proposed a notion of proof for Boolean equation systems they call support sets. We show that an adapted notion of support sets called proof graphs gives an alternative characterisation of the solution to a PBES, and prove that minimising proof graphs is NP-hard. Finally, we explain how proof graphs may be used in practice and illustrate how they can be used in equivalence checking to generate distinguishing formulas.