bisimulation-based verification

This paper addresses the long-standing problem that bisimulation—a fundamental notion in modal logic—lacks an object-language expression. To resolve this, we introduce a novel method for internalizing bisimulation: extending the basic modal language with a binary modality [b], interpreted directly over pairs of states within a single Kripke model to capture bisimilarity. Through semantic construction and axiomatic techniques, we develop the first sound and complete axiomatization for bisimulation over Kripke model pairs, taking [b] as a primitive operator. This constitutes the first fully object-language internalization of bisimulation, eliminating reliance on external model comparison. The resulting system provides a formal, proof-theoretic framework for meta-theoretic analysis of modal logic, enabling syntactic reasoning about structural equivalence between states.

Existing approaches to verifying timed bisimulation for timed automata lack interpretability and are unable to generate witnesses or counterexamples. This work proposes a novel zone-based construction method grounded in an extended fictitious-clock semantics, integrated with compositional symbolic representations. For the first time, this approach enables the automatic generation of semantically valid witnesses in the case of equivalence, or concrete behavioral counterexamples demonstrating divergence when systems are inequivalent—all while preserving decision correctness. By unifying timed automata theory, symbolic model checking, and timed bisimulation algorithms, the method not only achieves efficient equivalence checking but also provides interpretable evidence to support system refinement, testing, and formal verification.

This paper addresses the lack of semantic unification for simulation and bisimulation across heterogeneous concurrent systems—including probabilistic, weighted, neighborhood, and game-based models. We propose a functor-category-theoretic universal algebraic framework: system types are abstracted as set functors, and (bi)similarity is derived via relation liftings (relators). Our contributions are threefold: (1) We prove, for the first time, that 1/4-iso pullbacks preserving functors admit complete bisimulations induced by coBarr relators; (2) We establish precise equivalences between key relator properties—e.g., monotonicity and diagonal preservation—and closure properties of simulations; (3) We construct the maximal lax extension of inverse-image-preserving functors and introduce “twisted bisimulation”, yielding a strictly coarser, yet sound and complete, behavioral equivalence on labeled transition systems—thereby extending the expressive boundaries of simulation theory.

This work addresses model checking of nondeterministic transition systems against branching-time temporal logic CTL* (without the next operator X), extending bisimulation learning—previously limited to deterministic systems and linear-time logic (LTL). Methodologically, we propose an inductive decision-tree–based framework for bounded bisimulation learning, integrating SMT-driven validity checking of candidate bisimulation relations and an iterative training scheme tailored to well-founded bisimulation, yielding compact, verifiable stutter-insensitive quotient systems. Contributions include: (1) the first fully automated, sound-and-complete bisimulation learning algorithm supporting CTL* verification; (2) superior performance over state-of-the-art CTL/CTL* tools on benchmarks from concurrent software, protocols, and robotics; and (3) scalability to extremely large and even countably infinite-state systems, with LTL checking performance competitive with mature industrial tools.

This paper addresses the lack of a unified behavioral equivalence theory for heterogeneous systems—such as nondeterministic, probabilistic, and game-based systems. To this end, it proposes the first coalgebraic framework for heterogeneous (bi)simulation grounded in universal coalgebra. The core methodological innovation is the introduction of “relational connectors” between functors, serving as bridges for behavioral relations across system types, and systematically defining their composition, inversion, and identity operations. By integrating Kantorovich liftings and Barr extensions, the framework establishes a dual interpretation of modal logic and generalizes the Hennessy–Milner theorem, proving full correspondence between heterogeneous bisimilarity and logical equivalence on finitely branching systems. The framework uniformly characterizes behavioral consistency across labeled transition systems, probabilistic systems, and I/O conformance testing, thereby providing a foundational tool for verification of multi-paradigm systems.

This work addresses the challenge of effectively integrating axiomatic program logics into refinement-based proofs to verify that implementations satisfy safety specifications. We present the first systematic unification of Hoare logic, Incorrectness Logic, Lisbon Logic, and Necessary Precondition Logic, establishing their correspondence with forward and backward simulation relations. Crucially, we reduce the verification of these simulation relations to the validity of standard program logic triples, thereby enabling refinement proofs to directly leverage existing verification tools. As a practical demonstration, we successfully propagate the safety bound of an atomic sequential counter through an intermediate concurrent model to its Left-Right concurrent implementation, confirming both the practicality and effectiveness of our framework.

Standard simulation techniques struggle to verify liveness properties, and existing notions of fair simulation are often too complex for interactive verification. This work proposes a family of “approximate fair simulation” relations tailored to transition systems equipped with Büchi fairness conditions. By simplifying the nested inductive–coinductive structures inherent in traditional approaches, our method introduces a stronger and more user-friendly reasoning mechanism. We formalize this framework within a fixed-point logic and develop a corresponding deductive system, which we mechanize and prove correct in the Rocq proof assistant. Case studies demonstrate the effectiveness and practicality of our approach for interactive verification of fairness properties.

This study addresses the limitations of coinductive formalizations of interaction trees in the Rocq theorem prover, specifically their high complexity and the difficulty of proving equivalences for non-terminating programs. To overcome these challenges, this work proposes a domain-theoretic formalization framework that eschews built-in coinduction mechanisms. Instead, it defines program equivalence through inductive reasoning over terminating approximations, thereby circumventing coinductive pitfalls and simplifying the treatment of monad laws. As a key demonstration, the framework successfully verifies the equivalence of programs encoding the Syracuse sequence—a property whose termination is equivalent to an open mathematical conjecture. This result substantiates the effectiveness and practicality of the proposed approach in rigorously handling the semantics of non-terminating computations within interactive theorem proving environments.

This work investigates formal verification and runtime monitoring of properties in concurrent systems based on limited behavioral observations, such as traces or simulations. By introducing point-set topological methods, it establishes a precise correspondence between the topology induced by different observation mechanisms on the space of processes and verifiability: precisely those properties that are open sets in the respective topology are verifiable. The main contributions include a general verification theorem unifying monitorability under trace, simulation, and finite-depth bisimulation semantics; a rigorous proof that the topologies τ_O and τ_sim, induced respectively by observational closure and simulation relations, satisfy a strict inclusion τ_sim ⊂ τ_O; and the insight that stronger behavioral equivalences yield fundamentally distinct topologies, thereby deepening the understanding of the relationship between behavioral semantics and verification capabilities.

This work addresses the challenge in safety-critical systems where complexity hinders development teams from fully comprehending system behavior and providing trustworthy explanations. To bridge this gap, the paper proposes Behavior-Driven Explainability (BDX), a method that directly translates structured scenarios from Behavior-Driven Development (BDD) into formal behavioral specifications and automatically generates user-oriented explainable outputs. BDX seamlessly integrates system specification with explanation generation, making it applicable across any development phase and abstraction level. The approach is validated through a case study on exception handling in a RISC-V processor, demonstrating that BDX effectively supports explainability requirements early in the design process, thereby significantly enhancing system transparency and trustworthiness.