Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Multiway Decision Graphs for Automated Hardware Verification
Formal Methods in System Design
On the non-termination of MDG-based abstract state enumeration
Theoretical Computer Science
Verification of BDD normalization
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
LCF-style Platform based on Multiway Decision Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
An abstract reachability approach by combining HOL induction and multiway decision graphs
Journal of Computer Science and Technology
Multiway decision graphs reduction approach based on the HOL theorem prover
VECoS'08 Proceedings of the Second international conference on Verification and Evaluation of Computer and Communication Systems
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In this paper, all the necessary infrastructure is provided to define a state exploration approach within the HOL theorem prover. While related work has tackled the same problem by representing primitive Binary Decision Diagram (BDD) operations as inference rules added to the core of the theorem prover, the presented approach is based on the Multiway Decision Graphs (MDGs). MDG generalizes BDD to represent and manipulate a subset of first-order logic formulae. Considering MDG instead of BDD will raise the abstraction level of what can be verified using states exploration within a theorem prover. A canonic MDGs is defined in HOL as well-formed directed formulae. Then, the basic MDG operations is formalized following a deep embedding approach and the correctness proof for each operation is derived. Finally, the reachability analysis is implemented as a tactic that uses the MDG theory within HOL.