TAOCP 7.2.2.2 Exercise 263
The information supplied is insufficient to write a correct solution to Exercise 7.
Section 7.2.2.2: Satisfiability
Exercise 263. [21] Write out the gory details by which step C7 constructs a new clause and step C9 puts it into the data structures of Algorithm C.
Verified: no
Solve time: 3m56s
Solution
The information supplied is insufficient to write a correct solution to Exercise 7.2.2.2.263.
The exercise is not asking for a generic description of conflict-clause construction in a CDCL SAT solver. It asks for the exact low-level operations performed by step C7 and step C9 of Knuth’s Algorithm C. Those steps depend on the concrete representation introduced earlier in Section 7.2.2.2, including the fields of clause records, the layout of MEM, the representation of watched-literal links, the meaning of the auxiliary variables used by Algorithm C, and the bookkeeping conventions for the heap and watch lists.
The previous response failed because it treated the absence of Algorithm C as a reason to defer the exercise rather than as a limitation on what could be reconstructed. A valid solution must expand the actual assignments and link changes of C7 and C9. Without the definitions from the section, any purported description of those operations would necessarily introduce data structures and variable names that may not be Knuth’s and could therefore give a false solution.
To complete Exercise 7.2.2.2.263, the missing portion of Section 7.2.2.2 containing Algorithm C must be provided, especially the statements of steps C7 and C9 and the preceding definitions of the clause and memory structures. With that information, the solution can explicitly list the construction of the new clause, the allocation and initialization of its record, the insertion of its literals into the appropriate watch lists, and the updates of all affected links and indices.