Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

Abstract

Satisfiability Modulo Theories (SMT) solvers have emerged as prominent tools in formal methods applications. While originally targeted towards quantifier-free inputs, SMT solvers are now often used for handling quantified formulas in automated theorem proving and software verification applications. The most common technique for handling quantified formulas in modern SMT solvers in quantifier instantiation. This paper gives an overview of recent advances in quantifier instantiation in SMT. In addition to the well-known technique known as E-matching, we discuss the use of conflicts and models for accelerating the search for (un)satisfiably. We further mention new instantiation-based techniques that are specialized to background theories such as linear real and integer arithmetic, and future work in this direction.

The CADE-26 automated theorem proving system competition – CASC-26

“…In terms of numbers of problems solved there is clear evidence of progress in this important area of ATP, with four of this year's systems solving more problems than CVC4 1.4. In particular, CVC4 1.5 has improved greatly over CVC4 1.4, due to the addition of a new instantiation-based technique [7] that was optimized for quantifiers in pure linear arithmetic, and improved implementations of the various E-matching techniques that are effective on problems combining arithmetic with function symbols. The importance of TFA problems in application domains is growing, and this division will be emphasized in CASC-J8 (the next CASC).…”

Challenges for Fast Synthesis Procedures in SMT

“…It is often orders of magnitude faster than enumerative syntax-guided techniques, as reported in [23] and corroborated by the 2015 edition of the syntax-guided synthesis competition [2], where its implementation in the SMT solver CVC4 won both the general and conditional linear arithmetic tracks.…”

“…Previous work [23] has shown that SMT solvers with for support quantifier instantiation already have many of the functionalities required for synthesis. In particular, [23] describes a method to efficiently solve a common class of synthesis conjectures whose properties are single-invocation.…”

“…In particular, [23] describes a method to efficiently solve a common class of synthesis conjectures whose properties are single-invocation. The conjecture…”

“…In previous work [23], we presented two methods for tackling this problem that build on existing capabilities of SMT solvers:…”