Abstract
Assumption based SAT solving is an essential tool in many applications of SAT solving, especially in incremental SAT solving. For example, assumption based SAT solving is used when solving MaxSat, when computing minimal unsatisfiable subsets and minimal correction sets, and in various inductive verification applications. The MiniSat SAT solver introduced a simple technique for extending a SAT solver to allow it to handle assumptions by forcing the SAT solver to make the assumed literals its initial decisions. This approach persists in almost all current SAT solvers making it the most commonly used technique for handling assumptions. In this paper we explain some deficiencies in this approach that can hinder its efficiency, and provide a very simple modification that fixes these deficiencies. We show that our modification makes a non-trivial difference in practice, e.g., allowing two tested state of the art MaxSat solvers to solve 50+ new instances. This improvement is particularly useful since our modification is extremely simple to implement. We also examine the issue of repeated work when the solver backtracks over the assumptions, e.g., on restarts or when a new unit clause is learnt, and develop a new method for avoiding this repeated work that addresses some deficiencies of prior approaches.
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Notes
- 1.
Quick checks to determine if C is already satisfied can be made first by checking data in the watch data structure (the blocking literal) and checking if the clause’s other watch is \( true \).
- 2.
This description follows the MiniSat and Glucose schemes for watch literals, but this particular type of implementation is not necessary. Scanning \(O(n^2)\) literals in the clause down a single branch occurs with any implementation that stores no information about the previous scan [17].
- 3.
It is not clear if this third technique is an improvement outside of the context of MUS extraction.
- 4.
We save a reference to the reason clause, so before checking to see if the reason is still unit we must ensure that the references haven’t been changed by garbage collection, and that the implied literal is still at position zero in the reason clause (this is a MiniSat invariant for reason clauses).
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Hickey, R., Bacchus, F. (2019). Speeding Up Assumption-Based SAT. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_11
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