Exact Bayesian Inference for Loopy Probabilistic Programs

We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded looping behaviors. Our method is built on an extended denotational semantics represented by probability generating functions, which resolves semantic intricacies induced by intertwining discrete probabilistic loops with conditioning (for encoding posterior observations). We implement our method in a tool called Prodigy; it augments existing computer algebra systems with the theory of generating functions for the (semi-)automatic inference and quantitative verification of conditioned probabilistic programs. Experimental results show that Prodigy can handle various infinite-state loopy programs and outperforms state-of-the-art exact inference tools over benchmarks of loop-free programs

Encoding inductive invariants as barrier certificates: synthesis via difference-of-convex programming

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over an infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses unbounded-time safety of differential dynamical systems. The proposed condition is the weakest possible one to attain inductive invariance. We show that discharging the invariant barrier-certificate condition -- thereby synthesizing invariant barrier certificates -- can be encoded as solving an optimization problem subject to bilinear matrix inequalities (BMIs). We further propose a synthesis algorithm based on difference-of-convex programming, which approaches a local optimum of the BMI problem via solving a series of convex optimization problems. This algorithm is incorporated in a branch-and-bound framework that searches for the global optimum in a divide-and-conquer fashion. We present a weak completeness result of our method, namely, a barrier certificate is guaranteed to be found (under some mild assumptions) whenever there exists an inductive invariant (in the form of a given template) that suffices to certify safety of the system. Experimental results on benchmarks demonstrate the effectiveness and efficiency of our approach.Comment: To be published in Inf. Comput. arXiv admin note: substantial text overlap with arXiv:2105.1431

Effects of Constructivist and Transmission Instructional Models on Mathematics Achievement in Mainland China: A Meta-Analysis

The innovation of teaching and learning methods has been a common theme among these meta-analyses in the field of mathematics education. However, no published study has reviewed the effects of teaching models on mathematics achievement in mainland China. This review is intended to examine effects of constructivist instructional models and improved transmission instructional models on mathematics performance in mainland China. Using rigorous inclusion criteria, we identified 89 studies for constructivist instruction and 25 studies for improved transmission instruction in grades 1–12. Compared with traditional transmission instruction, the weighted mean effect sizes of constructivist instruction and improved transmission instruction were +0.55 and +0.63, respectively. These two effect sizes were not significantly different. Of the included studies, inquiry-based learning (N = 26, d = +0.52), problem-based learning (N = 21, d = +0.58), cooperative learning (N = 14, d = +0.67), autonomous learning (N = 8, d = +0.43), and script-based learning (N = 12, d = +0.47) were frequently used constructivist models, and grouping teaching (N = 10, d = +0.57) and variation teaching (N = 7, d = +0.49) were frequently used improved transmission models. All seven models had significant effects on improving mathematics achievement. Our findings implicate that the traditional transmission teaching model needs to be changed in mainland China but the constructivist model is not the only promising approach. The impact of study features and the limitations of this review were also discussed

Lower Bounds for Possibly Divergent Probabilistic Programs

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish non-trivial lower bounds on, e.g., termination probabilities and expected values, for possibly divergent probabilistic loops, e.g., the well-known three-dimensional random walk on a lattice

Two-stage Neural Network for ICASSP 2023 Speech Signal Improvement Challenge

In ICASSP 2023 speech signal improvement challenge, we developed a dual-stage neural model which improves speech signal quality induced by different distortions in a stage-wise divide-and-conquer fashion. Specifically, in the first stage, the speech improvement network focuses on recovering the missing components of the spectrum, while in the second stage, our model aims to further suppress noise, reverberation, and artifacts introduced by the first-stage model. Achieving 0.446 in the final score and 0.517 in the P.835 score, our system ranks 4th in the non-real-time track.Comment: Accepted by ICASSP 202

PA-Boot: A Formally Verified Authentication Protocol for Multiprocessor Secure Boot

Hardware supply-chain attacks are raising significant security threats to the boot process of multiprocessor systems. This paper identifies a new, prevalent hardware supply-chain attack surface that can bypass multiprocessor secure boot due to the absence of processor-authentication mechanisms. To defend against such attacks, we present PA-Boot, the first formally verified processor-authentication protocol for secure boot in multiprocessor systems. PA-Boot is proved functionally correct and is guaranteed to detect multiple adversarial behaviors, e.g., processor replacements, man-in-the-middle attacks, and tampering with certificates. The fine-grained formalization of PA-Boot and its fully mechanized security proofs are carried out in the Isabelle/HOL theorem prover with 306 lemmas/theorems and ~7,100 LoC. Experiments on a proof-of-concept implementation indicate that PA-Boot can effectively identify boot-process attacks with a considerably minor overhead and thereby improve the security of multiprocessor systems.Comment: Manuscript submitted to IEEE Trans. Dependable Secure Compu