Abstract In the last decade, numerous algorithms for single-objective Boolean optimization have been proposed that rely on the iterative usage of a highly effective Propositional Satisfiability (SAT) solver. But the use of SAT solvers in Multi-Objective Combinatorial Optimization (MOCO) algorithms is scarce. Due to the shortage of efficient tools for MOCO, many real-world applications formulated as multi-objective are cast as single-objective, using either a linear combination or by setting a preference order among the objectives. In this paper, we extend the state of the art of MOCO solvers with three novel unsatisfiability-based algorithms. The first two are core-guided MOCO solvers. The third is a hitting set MOCO solver. Experimental results in several sets of benchmark instances show that our new unsatisfiability-based algorithms can outperform and complement other SAT-based, state-of-the-art algorithms for MOCO.

Abstract In the article we show what a Dynamic Geometry Environment (DGE) and Computer Algebra System (CAS) software is capable of exploring, computing and proving a geometry problem that is closely related to the well-known Wallace-Simson theorem. In our case, this problem turns out to be quite difficult for some software tools incorporated in the DGE software. The computation of a searched locus by the software works well in our case, but the problem must be formulated in a specific way. In addition to the conclusions attained by DGE software, we present computer-aided analytical solutions in the second half of paper. It is shown that the use of non-degeneracy conditions before elimination leads to a significant reduction of the computation time.

Benchmarking is crucial for developing new algorithms. This also applies to solvers for the propositional satisfiability (SAT) problem. Benchmark selection is about choosing representative problem instances that reliably discriminate solvers based on their runtime. In this paper, we present a dynamic benchmark selection approach based on active learning. Our approach estimates the rank of a new solver among its competitors, striving to minimize benchmarking runtime but maximize ranking accuracy. Instead of using real-valued solver runtimes, our approach works with discretized runtime labels, which yielded better solver rank predictions. We evaluated this approach on the Anniversary Track dataset from the SAT Competition 2022. Our benchmark selection approach can predict the rank of a new solver after approximately 10 % of the time it would take to run the solver on all instances of this dataset, with a prediction accuracy of approximately 92 %. Additionally, we discuss the importance of instance families in the selection process. In conclusion, our tool offers a reliable method for solver engineers to assess a new solver’s performance efficiently.

Multiparty session types is a typing discipline used to write specifications, known as global types, for branching and recursive message-passing systems. A necessary operation on global types is projection to abstractions of local behaviour, called local types. Typically, this is a computable partial function that given a global type and a role erases all details irrelevant to this role. Computable projection functions in the literature are either unsound or too restrictive when dealing with recursion and branching. Recent work has taken a more general approach to projection defining it as a coinductive, but not computable, relation. Our work defines a new computable projection function that is sound and complete with respect to its coinductive counterpart and, hence, equally expressive. All results have been mechanised in the Coq proof assistant.

Deciding the satisfiability of formulas involving both quantifiers and theory defined symbols is a challenge in automated reasoning. This article presents an algorithm, called QSMA (Quantified Satisfiability Modulo Assignment), for the satisfiability of an arbitrary quantified formula modulo a complete theory and an initial assignment. The algorithm is proved partially correct and terminating, so that its total correctness is established. An optimized variant called OptiQSMA is also described and shown to preserve both partial correctness and termination. OptiQSMA is implemented in the YicesQS solver. OptiQSMA enabled YicesQS to achieve top of the line results, especially in linear rational arithmetic, in the 2022, 2023, and 2024 editions of the International Satisfiability Modulo Theories Competition (SMT-COMP). A report on these results in four fragments of arithmetic (LRA—Linear Rational Arithmetic, LIA—Linear Integer Arithmetic, NRA—Nonlinear Real Arithmetic, and NIA—Nonlinear Integer Arithmetic) and in the theory of bitvectors (BV) is included.

The article Interpolation and SAT-Based Model Checking (McMillan in: Proc. CAV 2003, LNCS, Springer [56]) describes a formal-verification algorithm, which was originally devised to verify safety properties of finite-state transition systems. It derives interpolants from unsatisfiable BMC queries and collects them to construct an overapproximation of the set of reachable states. Although 20 years old, the algorithm is still state-of-the-art in hardware model checking. Unlike other formal-verification algorithms, such as or PDR, which have been extended to handle infinite-state systems and investigated for program analysis, McMillan’s interpolation-based model-checking algorithm from 2003 has not been used to verify programs so far. Our contribution is to close this significant, two decades old gap in knowledge by adopting the algorithm to software verification. We implemented it in the verification framework CPAchecker and evaluated the implementation against other state-of-the-art software-verification techniques on the largest publicly available benchmark suite of C safety-verification tasks. The evaluation demonstrates that McMillan’s interpolation-based model-checking algorithm from 2003 is competitive among other algorithms in terms of both the number of solved verification tasks and the run-time efficiency. Our results are important for the area of software verification, because researchers and developers now have one more approach to choose from.

We present a stepwise refinement approach to develop verified parallel algorithms, down to efficient LLVM code. The resulting algorithms’ performance is competitive with their counterparts implemented in C++. Our approach is backwards compatible with the Isabelle Refinement Framework, such that existing sequential formalizations can easily be adapted or re-used. As case study, we verify a parallel quicksort algorithm that is competitive to unverified state-of-the-art algorithms.