Abstract Satisfiability Modulo Theories (SMT) solvers are widely used in formal verification. In program analysis, users often encounter queries that differ only by simple syntactic mutations and are logically equivalent. These mutations typically include assertion reordering, symbol renaming, anti-symmetric relation inversion, and commutative operand reordering. However, such minor changes can cause runtimes to vary by orders of magnitude. This variability reduces the predictability required for industrial-scale verification and remains a critical challenge. This paper presents SMTStabilizer, a tool that improves the stability of SMT solvers via context-driven normalization. Since complete input normalization is as hard as the graph isomorphism problem, SMTStabilizer adopts an approximate normalization strategy to avoid the high cost of exact normalization. The framework converts formulas into a structured representation and propagates structural information across nodes, enabling each node to capture its surrounding context. Using this context information, SMTStabilizer derives a consistent ordering over subformulas. This process yields a nearly canonical form that remains consistent across isomorphic inputs. SMTStabilizer also leverages pruning techniques that exploit the syntactic structure of SMT formulas to reduce normalization time. Evaluation on millions of queries using Z3 and cvc5 shows that SMTStabilizer improves solver stability to over $$98\%$$ 98 % under 10 random mutations.

Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion logic and a program logic specifically crafted for QEC programs and establish a sound proof system. We then develop an efficient method for handling verification conditions (VCs) of QEC programs: for Pauli errors, the VCs are reduced to classical assertions that can be solved by SMT solvers, and for non-Pauli errors, we provide a heuristic algorithm. We formalize the proposed program logic in Coq proof assistant, making it a verified QEC verifier. Additionally, we implement an automated QEC verifier, Veri-QEC, for verifying various fault-tolerant scenarios. We demonstrate the efficiency and broad functionality of the framework by performing different verification tasks across various scenarios. Finally, we present a benchmark of 14 verified stabilizer codes.

Abstract. Snapshot compressive imaging (SCI) refers to the recovery of three-dimensional data cubes, such as videos or hyperspectral images, from their two-dimensional projections, which are generated by a special encoding of the data with a mask. SCI systems commonly use binary-valued masks that follow certain physical constraints. Optimizing these masks subject to these constraints is expected to improve system performance. While prior theoretical analysis of SCI systems has primarily focused on independent and identically distributed Gaussian masks, recent empirical, data-driven mask optimizations yield structured and sometimes interpretable patterns. However, such empirical optimizations typically involve computationally intensive joint procedures that are expected to be suboptimal due to the nonconvexity and complexity of the optimization. In this paper, we analytically characterize the performance of SCI systems employing binary masks and leverage our analysis to optimize hardware parameters. Our findings provide a comprehensive and fundamental understanding of the role of binary masks, with both independent and dependent elements, and their optimization. We also present simulation results that confirm our theoretical findings and further illuminate different aspects of mask design.

Abstract Satisfiability Modulo Theories on arithmetic theories have significant applications in many important domains. Previous efforts have been mainly devoted to improving the techniques and heuristics in sequential SMT solvers. With the development of computing resources, a promising direction to boost performance is parallel and even distributed SMT solving. We explore this potential in a divide-and-conquer view and propose a novel dynamic parallel framework with variable-level partitioning. To the best of our knowledge, this is the first attempt to perform variable-level partitioning for arithmetic theories. Moreover, we enhance the interval constraint propagation algorithm, coordinate it with Boolean propagation, and integrate it into our variable-level partitioning strategy. Our partitioning algorithm effectively capitalizes on propagation information, enabling efficient formula simplification and search space pruning. We apply our method to three state-of-the-art SMT solvers, namely CVC5, OpenSMT2, and Z3, resulting in efficient parallel SMT solvers. Experiments are carried out on benchmarks of linear and non-linear arithmetic over both real and integer variables, and our variable-level partitioning method shows substantial improvements over previous partitioning strategies and is particularly good at non-linear theories.

Abstract MaxSAT modulo theories (MaxSMT) is an important generalization of Satisfiability modulo theories (SMT) with various applications. In this paper, we focus on MaxSMT with the background theory of Linear Integer Arithmetic, denoted as MaxSMT(LIA). We design the first local search algorithm for MaxSMT(LIA) called PairLS, based on the following novel ideas. A novel operator called pairwise operator is proposed for integer variables. It extends the original local search operator by simultaneously operating on two variables, enriching the search space. Moreover, a compensation-based picking heuristic is proposed to determine and distinguish the pairwise operations. Experiments are conducted to evaluate our algorithm on massive benchmarks. The results show that our solver is competitive with state-of-the-art MaxSMT solvers. Furthermore, we also apply the pairwise operation to enhance the local search algorithm of SMT, which shows its extensibility.

The Guaranteed Delivery (GD) advertising is a crucial component of the online advertising industry, and the allocation of inventory in GD advertising is an important procedure that influences directly the ability of the publisher to fulfill the requirements and increase its revenues. Nowadays, as the requirements of advertisers become more and more diverse and fine-grained, the focus ratio requirement, which states that the portion of allocated impressions of a designated contract on focus media among all possible media should be greater than another contract, often appears in business scenarios. However, taking these requirements into account brings hardness for the GD advertising inventory allocation as the focus ratio requirements involve non-convex multilinear constraints. Existing methods which rely on the convex properties are not suitable for processing this problem, while mathematical programming or constraint-based heuristic solvers are unable to produce high-quality solutions within the time limit. Therefore, we propose a local search framework to address this challenge. It incorporates four new operators designed for handling multilinear constraints and a two-mode algorithmic architecture. Experimental results demonstrate that our algorithm is able to compute high-quality allocations with better business metrics compared to the state-of-the-art mathematical programming or constraint based heuristic solvers. Moreover, our algorithm is able to handle the general multilinear constraints and we hope it could be used to solve other problems in GD advertising with similar requirements.

Snapshot compressive imaging (SCI) recovers high-dimensional (3D) data cubes from a single 2D measurement, enabling diverse applications like video and hyperspectral imaging to go beyond standard techniques in terms of acquisition speed and efficiency. In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure. Such UNN-based methods are appealing as they have the potential of avoiding the computationally intensive retraining required for different source models and different measurement scenarios. We first develop a theoretical framework for characterizing the performance of such UNN-based methods. The theoretical framework, on the one hand, enables us to optimize the parameters of data-modulating masks, and on the other hand, provides a fundamental connection between the number of data frames that can be recovered from a single measurement to the parameters of the untrained NN. We also employ the recently proposed bagged-deep-image-prior (bagged-DIP) idea to develop SCI Bagged Deep Video Prior (SCI-BDVP) algorithms that address the common challenges faced by standard UNN solutions. Our experimental results show that in video SCI our proposed solution achieves state-of-the-art among UNN methods, and in the case of noisy measurements, it even outperforms supervised solutions. Code is publicly available at [https://github.com/Computational-Imaging-RU/SCI-BDVP](https://github.com/Computational-Imaging-RU/SCI-BDVP).

Facing the implementation problems such like low growth reward, long training time, and poor stability of the multiagent learning methods when dealing with complex environment and more agents, this paper proposes a fast optimal coordination method for multiagent in complex environment (FOC-MACE). Firstly, the environment exploration strategy is introduced into the policy network based on the MADDPG method for higher growth rewards. Then, the parallel computing technology is adopted in the critic network, in purpose to effectively reduce the training time. These tactics together are beneficial to enhance the stability of multiagent learning. Lastly, the optimal resource allocation is carried out to realize optimal coevolution of the multiagents and further improve the learning ability of the agents’ group. To verify the effectiveness of our proposal, the FOC-MACE is compared with several advanced methods at current stage in the MPE environment. Three different experiments prove that by using our method, the growth reward is increased by up to 37.1%, the training is speed up significantly, and the stability of the method, which represented by standardized variance, is also improved. In addition, this paper validated the fast optimal coordination method for multiagent systems in the context of UAV scenarios, demonstrating the practical performance of the approach. Through comprehensive experiments and scenario validations, the study successfully confirmed the effectiveness of the proposed fast optimal coordination method for multiagent systems in complex environments.

The maximum quasi-clique problem (MQCP) is an important extension of maximum clique problem with wide applications. Recent heuristic MQCP algorithms can hardly solve large and hard graphs effectively. This paper develops an efficient local search algorithm named NuQClq for the MQCP, which has two main ideas. First, we propose a novel vertex selection strategy, which utilizes cumulative saturation information to be a selection criterion when the candidate vertices have equal values on the primary scoring function. Second, a variant of configuration checking named BoundedCC is designed by setting an upper bound for the threshold of forbidding strength. When the threshold value of vertex exceeds the upper bound, we reset its threshold value to increase the diversity of search process. Experiments on a broad range of classic benchmarks and sparse instances show that NuQClq significantly outperforms the state-of-the-art MQCP algorithms for most instances.