Abstract The IC3 algorithm, also known as PDR, is a SAT-based model checking algorithm that has significantly influenced the field in recent years due to its efficiency, scalability, and completeness. It utilizes SAT solvers to solve a series of SAT queries associated with relative induction. In this paper, we introduce several optimizations for the SAT solver in IC3 based on our observations of the unique characteristics of these SAT queries. By observing that SAT queries do not necessarily require decisions on all variables, we compute a subset of variables that need to be decided before each solving process while ensuring that the result remains unaffected. Additionally, noting that the overhead of binary heap operations in VSIDS is non-negligible, we replace the binary heap with buckets to achieve constant-time operations. Furthermore, we support temporary clauses without the need to allocate a new activation variable for each solving process, thereby eliminating the need to reset solvers. We developed a novel lightweight CDCL SAT solver, GipSAT, which integrates these optimizations. A comprehensive evaluation highlights the performance improvements achieved by GipSAT. Specifically, the GipSAT-based IC3 demonstrates an average speedup of $$3.61$$ 3.61 times in solving time compared to the IC3 implementation based on MiniSat.

Model checking is an automated method used to formally verify systems by checking them against properties. However, a major problem in model checking is the state explosion. To overcome this challenge, one approach is to utilize parallel processing capabilities to either speed up computations or handle larger-scale problems. Explicit model checking has lower computational complexity and can be easily parallelized. There are numerous parallel explicit model checking algorithms available in the literature. Symbolic model checking offers significant advantages over explicit model checking in terms of problem scalability and verification speed. However, treating states encountered during the search as sets poses a challenge in devising efficient parallel algorithms. As a result, current research on parallelizing symbolic model checking has primarily focused on reachability analysis or safety properties, rather than attempting to parallelize the nested fixpoint calculations. In this paper, we propose a novel property-driven approach for parallel symbolic model checking of full LTL. Our algorithm introduces a fair model state labelling function that forms a partition of the nested fixpoint across the product combining the model and the property Büchi automaton. The experimental results demonstrate significant speedup, ranging from 2.81 to 17.19 times compared to sequential approaches on a 32-core machine. Moreover, in comparison to existing parallel model checking methods, our approach not only surpasses those relying on BDD libraries with a maximum improvement of up to 134% and an average improvement of 33.1% but also demonstrates significant superiority over the state-of-theart parallel explicit model checker.

There is a growing demand for maps from government, enterprises and the pubulic. This paper studies the data management methods of ancient and modern maps to solve the problems of scattered storage, low openness, inconvenient query and use, lack of system inheritance and so on. Based on the digital processing and database management system, the map database was established after the ancient map was edited. Based on SOA service architecture and Browser/Server mode, the spatio-temporal fusion and operation platform for ancient and modern maps is established. The functions of map unified management, visual display, query and analysis, input and multi-mode export are achieved. Using Android and IOS technology to build mobile applications, improve map management and sharing application mode.