• Volume 13,Issue 3,2023 Table of Contents
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    • Preface to the Special Issue on Constraint Solving and Theorem Proving

      2023, 13(3):243-245. DOI: 10.21655/ijsi.1673-7288.00299

      Abstract (306) HTML (0) PDF 710.12 K (253) Comment (0) Favorites


    • UC-based Approximate Incremental Reachability

      2023, 13(3):247-267. DOI: 10.21655/ijsi.1673-7288.00302

      Abstract (269) HTML (0) PDF 2.71 M (230) Comment (0) Favorites

      Abstract:In recent years, formal verification technology has received more and more attention, and it plays an important role in ensuring the safety and correctness of systems in safety-critical areas. As a branch of formal verification with a high degree of automation, model checking has a very broad development prospect. This study analyzes and proposes a new model checking technique, which can effectively check transition systems, including bug-finding and safety proof. Different from existing model checking algorithms, the proposed method, Unsatisfiable Core (UC)-based Approximate Incremental Reachability (UAIR), mainly utilizes the UC to solve a series of candidate safety invariants until the final invariant is generated, so as to realize safety proof and bug-finding. In symbolic model checking based on the SAT solver, this study uses the UC obtained by the satisfiability solver to construct the candidate safety invariant, and if the transition system itself is safe, the obtained initial invariant is only an approximation of the safety invariant. Then, while checking the safety, the study incrementally improves the candidate safety invariant until it finds a true invariant that proves the system is safe; if the system is unsafe, the method can finally find a counterexample to prove the system is unsafe. The brand new method exploits UCs for safety model checking and achieves good results. It is known that there is no absolute best method in the field of model checking. Although the proposed method cannot surpass the current mature methods such as IC3 and complement Approximate Reachability (CAR), in terms of the number of solvable benchmarks, the method in this paper can solve three cases that other mature methods are unable to solve. It is believed that the method can be a valuable addition to the model checking toolset.

    • GC-MCR: Directed Graph Constraint-guided Concurrent Bug Detection Method

      2023, 13(3):269-296. DOI: 10.21655/ijsi.1673-7288.00300

      Abstract (316) HTML (0) PDF 4.62 M (263) Comment (0) Favorites

      Abstract:Constraint solving has been applied to many domains of program analysis and is further used in concurrent program analysis. Concurrent programs have been widely used with the rapid development of multi-core processors. However, concurrent bugs threaten the security and reliability of concurrent programs, and thus it is of great importance to detect concurrent bugs. The explosion of thread interleaving caused by the uncertainty of the execution of concurrent program threads brings some challenges to the detection of concurrent bugs. Existing concurrent defect detection algorithms reduce the exploration cost in the state space of concurrent programs by reducing invalid thread interleaving. For example, the maximal causal model algorithm transforms the state space exploration problem of concurrent programs into a constraint solving problem. However, it will produce a large number of redundant and conflicting constraints during constraint construction, which greatly prolongs the time of constraint solving, increases the number of constraint solver calls, and reduces the exploration efficiency of concurrent program state space. Thus, this study proposes a directed graph constraint-guided maximal causality reduction method, called GC-MCR. This method aims to improve the speed of constraint solving and the efficiency of the state space exploration of concurrent programs by filtering and reducing constraints using directed graphs. The experimental results show that the GC-MCR method can effectively optimize the expression of constraints, so as to improve the solving speed of the constraint solver and reduce the number of solver calls. Compared with the existing J-MCR method, GC-MCR can significantly improve the detection efficiency of concurrent program bugs without reducing the detection ability of concurrent bugs, and the test time on 38 groups of concurrent test programs widely used by existing research methods can be reduced by 34.01% on average.

    • Refinement-based Modeling and Formal Verification for Multiple Secure Partitions of TrustZone

      2023, 13(3):297-321. DOI: 10.21655/ijsi.1673-7288.00301

      Abstract (391) HTML (0) PDF 1.19 M (233) Comment (0) Favorites

      Abstract:As a trusted execution environment technology on ARM processors, TrustZone provides an isolated and independent execution environment for security-sensitive programs and data on the device. However, running the trusted OS and all the trusted applications in the same environment may cause problems---The exploitation of vulnerabilities on any component may affect the others in the system. Although ARM proposed the S-EL2 virtualization technology, which supports multiple isolated partitions in the secure world to alleviate this problem, there may still be security threats such as information leakage between partitions in the real-world partition manager. Current secure partition manager designs and implementations lack rigorous mathematical proofs to guarantee the security of isolated partitions. This study analyzes the multiple secure partitions architecture of ARM TrustZone in detail, proposes a refinement-based modeling and security analysis method for multiple secure partitions of TrustZone, and completes the modeling and formal verification of the secure partition manager in the theorem prover Isabelle/HOL. First, we build a multiple secure partitions model named RMTEE based on refinement: an abstract state machine is used to describe the system running process and security policy requirements, forming the abstract model. Then the abstract model is instantiated into the concrete model, in which the event specification is implemented following the FF-A specification. Second, to address the problem that the existing partition manager design cannot meet the goal of information flow security verification, we design a DAC-based inter-partition communication access control and apply it to the modeling and verification of RMTEE. Lastly, we prove the refinement between the concrete model and the abstract model, and the correctness and security of the event specification in the concrete model. The formalization and verification consist of 137 definitions and 201 lemmas (more than 11,000 lines of Isabelle/HOL code). The results show that the model satisfies confidentiality and integrity, and can effectively defend against malicious attacks on partitions.

    • Coq Formalization of ZFC Set Theory for Teaching Scenarios

      2023, 13(3):323-357. DOI: 10.21655/ijsi.1673-7288.00303

      Abstract (264) HTML (0) PDF 866.64 K (356) Comment (0) Favorites

      Abstract:Discrete mathematics is a foundation course for computer-related majors, and propositional logic, first-order logic, and the axiomatic set theory are important parts of this course. Teaching practice shows that beginners find it difficult to accurately understand abstract concepts, such as syntax, semantics, and reasoning system. In recent years, some scholars have begun introducing interactive theorem provers into teaching to help students construct formal proofs so that they can understand logic systems more thoroughly. However, directly employing the existing theorem provers will increase students' learning burden since these tools have a high threshold for getting started with them. To address this problem, we develop a prover for the Zermelo-Fraenkel set theory with the axiom of Choice (ZFC) in Coq for teaching scenarios. Specifically, the first-order logical reasoning system and the axiomatic set theory ZFC are formalized, and several automated proof tactics specific to reasoning rules are then developed. Students can utilize these automated proof tactics to construct formal proofs of theorems in a textbook-style concise proving environment. This tool has been introduced into the teaching of the course of discrete mathematics for freshmen. Students with no prior theorem-proving experience can quickly construct formal proofs of theorems including mathematical induction and Peano arithmetic with this tool, which verifies the practical effectiveness of this tool.

    • Consequence-based Axiom Pinpointing for Expressive Description Logic Ontologies

      2023, 13(3):359-374. DOI: 10.21655/ijsi.1673-7288.00304

      Abstract (420) HTML (0) PDF 1.80 M (224) Comment (0) Favorites

      Abstract:Axiom pinpointing has attracted extensive interest in Description Logics (DLs) due to its effect of exploring explicable defects in the DL ontology and searching for hidden justifications for logical implication. Balancing the expressive power of DLs and the solving efficiency of reasoners has always been the focus of axiom pinpointing research. This study, from both glass-box and black-box perspectives, proposes a consequence-based method for axiom pinpointing. The glass-box method uses modified consequence-based rules (pinpointing rules) to trace the specific process of inference and introduces the concept of pinpointing formula to establish the correspondence between the label of the Boolean formula and all the minimal axiom sets. The black-box method directly calls the reasoner based on the unmodified consequence-based rules and further uses the Hitting Set Tree (HST) to compute all justifications of logical implication. Finally, a reasoning tool is designed based on the two axiom pinpointing algorithms for expressive DL ontologies. Its feasibility is verified theoretically and experimentally, and its solving efficiency is compared with that of existing axiom pinpointing tools.