perform model checking

This work addresses three fundamental challenges in model checking—insufficient precision, state-space explosion, and spurious counterexamples—by systematically reducing model checking to program verification. Methodologically, we design MOKA, a domain-specific language that encodes ACTL and universal μ-calculus formulas as programs; within an abstract interpretation framework, we construct a Kleene algebraic semantic model and introduce locally complete abstractions coupled with counterexample-guided dynamic domain refinement, synergistically combining under-approximation and abstraction for controllable precision enhancement. Our contributions are threefold: (1) the first rigorous reduction of model checking to program verification under abstract interpretation; (2) support for non-partitioning abstractions, significantly reducing false positives; and (3) theoretical guarantees for complete detection of violating initial states. The resulting analyzer is general-purpose and precision-tunable.

This work addresses the model checking problem for Linear Temporal Logic (LTL) formulas under given prior knowledge ( K ), formalized as an LTL formula. We propose a knowledge-guided Büchi automaton simplification method: first constructing a knowledge automaton ( A_K ) from ( K ), then defining and implementing structural reduction of the negated property automaton ( A_{ egvarphi} ) with respect to ( A_K ), yielding an equivalent but significantly smaller Büchi automaton ( B ). Our approach enables direct verification—without constructing the full product automaton ( S otimes A_{ egvarphi} )—for approximately 50% of the MCC’22 benchmark instances. For the remaining cases, ( B ) exhibits substantially fewer states, accelerating emptiness checking. The core contribution lies in formally encoding prior LTL knowledge as an automaton and tightly integrating it into both automaton construction and reduction, thereby enabling semantics-aware acceleration of model checking.

This work addresses the lack of a unified and scalable theoretical framework for verifying concurrent programs under weak memory models. It proposes a novel approach that leverages monadic second-order logic (MSO) as a meta-theory, integrated with treewidth analysis of graph structures, to establish a uniform framework for verification and robustness checking. The study establishes, for the first time, an intrinsic connection between MSO axiomatizability and bounded treewidth, introduces the new notion of “reads-from robustness,” and proves that models such as TSO are not MSO-axiomatizable due to their unbounded treewidth. Building on these insights, the paper identifies several classes of weak memory models that are amenable to MSO axiomatization and provides either automated verification algorithms or methods for generating robustness counterexamples for them.

Existing model checkers struggle to simultaneously achieve sound safety verification and effective counterexample generation for programs containing long, input-dependent erroneous paths. This paper proposes the GPS algorithm, which formulates model checking as an abstraction-guided directed state-space search: lightweight path abstractions are generated via compositional static analysis to guide depth-first exploration; a two-level search strategy is designed to coordinate verification and falsification; and a customized, completeness-guaranteed instrumentation mechanism is introduced. GPS is the first approach to unify efficient counterexample discovery with rigorous refutation completeness. Evaluated on the SV-COMP benchmark, GPS increases the number of solved instances by 12.7% and reduces average runtime by 34.5%, significantly outperforming state-of-the-art tools.

This study investigates efficient representations of models of MSO₂ formulas with free variables over a given graph structure, where the representation size is controlled by structural parameters such as treewidth or pathwidth. Employing directed acyclic graph-based knowledge representation formalisms—specifically Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs)—in conjunction with parameterized complexity analysis, the work establishes that SDDs admit linear-size representations parameterized by treewidth, and OBDDs achieve linear size when parameterized by pathwidth. Conversely, it constructs counterexamples demonstrating that treewidth alone cannot bound OBDD size. These results extend Courcelle’s theorem from a representational perspective, establishing a theory of parameterized linear-size representations for MSO₂ models and forging a novel connection between parameterized algorithms and knowledge representation.

This work addresses the challenge of verifying graph-theoretic properties on graph classes with bounded treewidth or pathwidth by proposing a unified framework that integrates tree-decomposition-based dynamic programming with formal reductions of graph properties. The framework enables automatic verification of atomic properties and their Boolean combinations, achieving for the first time a modular composition of dynamic programming algorithms coupled with parameterized automated theorem proving in treewidth. The developed TreeWidzard engine automatically checks whether all graphs of treewidth at most \(k\) satisfy a given Boolean expression \(P\) over graph properties, significantly enhancing the scalability and automation of complex graph property verification.

This study investigates the fixed-parameter tractability (FPT) of first-order model checking when parameterized by the number of variables in the logical formula. Focusing on monotone and hereditary graph classes, the paper provides the first systematic characterization of graph classes that admit FPT algorithms: a complete characterization is established for monotone classes, while an approximate characterization is given for hereditary classes. By integrating techniques from parameterized complexity theory, first-order model checking, and structural graph analysis, the work precisely delineates the boundary of FPT tractability under variable-number parameterization, thereby significantly advancing the understanding of the parameterized complexity landscape of first-order model checking.

This work addresses the challenge of efficiently evaluating rich fragments of Counting Monadic Second-Order logic (CMSO) on topological minor-free graph classes, where existing methods fall short. We introduce a novel CMSO fragment that restricts set quantifiers to vertex sets of bounded monotone dimension and incorporates a disjoint-paths predicate. By leveraging a framework of annotated graph parameters together with structural graph theory, we extend such quantifier restrictions—previously limited to first-order logic—to topological minor-free classes for the first time. Our results establish fixed-parameter tractability of model checking for this fragment on these graph classes, thereby generalizing several classical meta-theorems beyond the expressive limits of first-order logic.

This work addresses the undecidability of formal verification for model transformations, which stems from Turing completeness, and the path explosion problem that persists even in non-Turing-complete domain-specific languages like DSLTrans. The authors propose a scalable verification approach by establishing, for the first time, a bounded completeness theorem for a fragment of DSLTrans with respect to existential and traceability properties, thereby reducing infinite verification problems to bounded yet complete checks. Their method integrates class-boundary-aware encoding, trace-aware dependency analysis, and a CEGAR-driven refinement strategy to drastically reduce SMT formula size and eliminate spurious counterexamples. Implemented atop Z3 and integrated into a Web IDE, the tool successfully verifies 552 out of 899 properties across 29 real-world transformations, generates 345 valid counterexamples, times out on only two cases, and achieves up to a 112× speedup on challenging instances through refinement.