Problem
Research questions and friction points this paper is trying to address.
SMT solving
Quantifier instantiation
Non-ground clause learning
CDCL(T)
Conflict analysis
Extending SMT Solving with Non-Ground Clause Learning
🤖 AI Summary
本文提出一种结合地面实例化、CDCL(T)风格规则和非地面冲突分析的演算法，以解决非地面SMT求解问题，该方法能生成更通用的学习子句。
📝 Abstract
Quantifier instantiation is currently the main approach to non-ground SMT solving: solvers generate ground instances and solve the resulting ground SMT problems with CDCL(T)-style reasoning. When a conflict is found, conflict analysis learns only a ground clause, even though the conflict comes from instances of non-ground clauses. Yet non-ground reasoning can give exponentially shorter proofs than purely ground reasoning. We propose a calculus that consists of ground instantiations, CDCL(T)-style rules, and non-ground conflict analysis. The solver reasons on ground instances, but the resolution steps of conflict analysis are performed on their original non-ground clauses. This produces learned clauses that are typically more general than the ground conflict. With a suitable strategy, the learned clauses are even non-redundant. We also show how chronological backtracking can be included in SMT solving. Our calculus gives a common setting for CDCL(T)-style SMT solving, a range of instantiation-based procedures, and non-ground clause learning, and we prove that it simulates CDCL, SCL(FOL), SCL(T), and even Resolution.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Non-Ground Clause Learning
Quantifier Instantiation
CDCL(T)
Conflict Analysis
Chronological Backtracking
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