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We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3 theorem prover. A crucial insight that underpins our algorithm is that real-world instances contain a wealth of information about upper and lower bounds on lengths of strings under constraints, and such information can be used very effectively to simplify operations on automata representing regular expressions. Additionally, we present a number of novel general heuristics, such as the prefix/suffix method, that can be used in conjunction with a variety of regex solving algorithms, making them more efficient. We showcase the power of our algorithm and heuristics via an extensive empirical evaluation over a large and diverse benchmark of 57256 regex-heavy instances, almost 75% of which are derived from industrial applications or contributed by other solver developers. Our solver outperforms five other state-of-the-art string solvers, namely, CVC4, OSTRICH, Z3seq, Z3str3, and Z3-Trau, over this benchmark, in particular achieving a 2.4x speedup over CVC4, 4.4x speedup over Z3seq, 6.4x speedup over Z3-Trau, 9.1x speedup over Z3str3, and 13x speedup over OSTRICH.
We give an overview of recent techniques for implementing syntax-guided synthesis (SyGuS) algorithms in the core of Satisfiability Modulo Theories (SMT) solvers. We define several classes of synthesis conjectures and corresponding techniques that can
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not sufficient. We
Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex n
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little
This extended abstract reports on current progress of SMTCoq, a communication tool between the Coq proof assistant and external SAT and SMT solvers. Based on a checker for generic first-order certificates implemented and proved correct in Coq, SMTCoq