On-the-fly resolve trace minimization

Abstract

The ability of modern SAT solvers to produce proofs of unsatisfiability for Boolean formulas has become a powerful tool for EDA applications. Proofs are generated from a resolve trace that captures information about the creation of all conflict clauses. Due to their sizes, resolve traces are kept in files. The sizes of these files makes the use of proofs of unsatisfiability impractical for industrial tools. Although only a small part of the resolve trace is eventually used, until now it was not known how to filter out unnecessary information.We propose a simple algorithm for on-the-fly resolve trace minimization in which we identify clauses that are guaranteed not to take part in the proof of unsatisfiability, and delete all of their associated information. This algorithm dramatically decreases the size of the resolve trace, to the point where it can be stored in the main memory. Our experiments reveal that the minimized trace is typically 3 to 6 times smaller. This makes the use of proofs of unsatisfiability and the computation of unsat cores more practical and will enable future applications to take advantage of it.

Using unsatisfiable cores to debug multiple design errors

“…Moreover, exploiting incremental SAT within our framework more efficiently by keeping detailed information about learned clauses [14] may further improve the performance.…”

“…For our purpose minimality is not necessary. A SAT solver can produce such an unsat core on the fly with a moderate overhead [14].…”

“…We start from the initial unsatisfiable SAT instance: the circuit is restricted to the failure trace and to correct output values [13]. A SAT solver is applied to extract an unsatisfiable core, i.e., a part of the SAT problem that is already unsatisfiable [4,21,14]. Then, the injection logic is activated within the unsatisfiable core to determine fault candidates or a next unsatisfiable core.…”

Computing bounds for fault tolerance using formal techniques

“…the clauses that are necessary to imply learned information. This information can efficiently be exploited at a higher level [20], [24], [25]. If the clauses, which establish the reason of a conflict, remain in the problem instance, the corresponding conflict clauses can be reused as well.…”

Accelerated Deletion-based Extraction of Minimal Unsatisfiable Cores

“…The problem for finding a small, a minimal (irreducible), the minimum (smallest minimal), or all the MUCs has been addressed frequently over the last decade [51,19,9,36,28,49,17,13,42,8,1,27,46,18,20,38,14,26,50,33,43,12,41,6,30,7,48,5,4,29,24,35,39] because of its theoretical and practical importance. The applications of MUC-extraction include abstraction refinement for model checking [31,21,4], formal equivalence verification [23,12] and functional bi-composition [25,10] -see [43,34] for extensive surveys.…”