2 research outputs found
Resolution Proof Transformation for Compression and Interpolation
Verification methods based on SAT, SMT, and Theorem Proving often rely on
proofs of unsatisfiability as a powerful tool to extract information in order
to reduce the overall effort. For example a proof may be traversed to identify
a minimal reason that led to unsatisfiability, for computing abstractions, or
for deriving Craig interpolants. In this paper we focus on two important
aspects that concern efficient handling of proofs of unsatisfiability:
compression and manipulation. First of all, since the proof size can be very
large in general (exponential in the size of the input problem), it is indeed
beneficial to adopt techniques to compress it for further processing. Secondly,
proofs can be manipulated as a flexible preprocessing step in preparation for
interpolant computation. Both these techniques are implemented in a framework
that makes use of local rewriting rules to transform the proofs. We show that a
careful use of the rules, combined with existing algorithms, can result in an
effective simplification of the original proofs. We have evaluated several
heuristics on a wide range of unsatisfiable problems deriving from SAT and SMT
test cases
Partial Regularization of First-Order Resolution Proofs
Resolution and superposition are common techniques which have seen widespread
use with propositional and first-order logic in modern theorem provers. In
these cases, resolution proof production is a key feature of such tools;
however, the proofs that they produce are not necessarily as concise as
possible. For propositional resolution proofs, there are a wide variety of
proof compression techniques. There are fewer techniques for compressing
first-order resolution proofs generated by automated theorem provers. This
paper describes an approach to compressing first-order logic proofs based on
lifting proof compression ideas used in propositional logic to first-order
logic. One method for propositional proof compression is partial
regularization, which removes an inference when it is redundant in the
sense that its pivot literal already occurs as the pivot of another inference
in every path from to the root of the proof. This paper describes the
generalization of the partial-regularization algorithm
RecyclePivotsWithIntersection [10] from propositional logic to first-order
logic. The generalized algorithm performs partial regularization of resolution
proofs containing resolution and factoring inferences with unification. An
empirical evaluation of the generalized algorithm and its combinations with the
previously lifted GreedyLinearFirstOrderLowerUnits algorithm [12] is also
presente