reachability analysis using multiway decision graphs in the hol theorem prover
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.
reachability analysis multiway decision graphs hol