apply process calculi

This paper addresses the verification of deadlock and resource contention in parallel processes within the π-calculus. We propose a novel logical characterization method: recursive- and race-free π-processes are modeled as sequent calculus derivations, yielding the first purely logical characterization of deadlock-freedom. By establishing a precise correspondence between process semantics and logical derivations, we obtain a concise, decidable logical criterion for deadlock-freedom. Moreover, we prove that all such processes admit faithful encodings into choreographic programs, thereby establishing strong completeness of choreography languages for concurrent behavior. These results extend the “computation-as-deduction” paradigm to concurrency verification, broadening its theoretical scope. Our approach provides a new foundation for logic-based verification of concurrent programs, bridging process calculi and proof theory in a principled manner.

This work addresses the formal modeling of interactive concurrent processes by proposing a multi-categorical parameterized term rewriting system. For the first time, process interaction is characterized as a confluent and terminating rewrite relation, and it is shown that the resulting term structures naturally form a virtual double category. The central contribution lies in the construction of a denotational semantic functor from this computational syntax to the free corner construction in free monoidal categories, thereby providing a rigorous semantic foundation and mathematical guarantee for interactive behavior.

This paper systematically compares two state-of-the-art deadlock-free type systems—HCP, based on hypersequential linear logic, and P, a priority-based asynchronous type system—to clarify their expressive power and fundamental differences in guaranteeing deadlock freedom for concurrent processes. Method: We formalize both systems under a unified asynchronous semantics and construct rigorous type mappings and process encodings between them. Contribution/Results: We establish, for the first time, that (1) the process classes accepted by HCP and P are incomparable, yet their intersection precisely characterizes strong deadlock-freedom; and (2) hypersequential structure does not enhance the deadlock-freedom verification capability of linear logic. All results are formally verified. This work deepens the theoretical understanding of static deadlock avoidance mechanisms and provides a foundational benchmark for the design and comparative analysis of deadlock-free type systems.

This paper systematically evaluates the quality of encodings between process calculi, specifically addressing the fidelity of two classical translations—from synchronous to asynchronous π-calculus—namely the Honda–Tokoro and Boudol encodings—under various behavioral equivalences. Method: We conduct a dual-dimensional verification within a unified formal framework, integrating Gorla’s five criteria for valid encodings with a hierarchy of semantic equivalences: trace equivalence, failure simulation, observational equivalence, and strong/weak bisimulation. Contribution/Results: Our analysis reveals that the Honda–Tokoro encoding satisfies only the weakest criterion—trace equivalence—whereas the Boudol encoding preserves the strictly stronger failure simulation equivalence, demonstrating significantly higher behavioral fidelity. This work establishes the first empirical benchmark for assessing encoding quality in process calculi and provides a reusable, principled methodology grounded in both syntactic validity criteria and semantic strength.

Standard session types over-rely on serialized structure, imposing redundant sequential constraints at the type level that obscure essential behavioral dependencies. Method: We introduce *minimal session types*, which retain only intra-process sequentiality necessary for correctness while eliminating all extraneous sequencing in the type system. Based on a higher-order concurrent session π-calculus, we develop a lossless compilation framework that translates any standard session-typed process into an equivalent minimally typed one. We further establish, for the first time, a typed version of Parrow’s three-prefix decomposition theorem, enabling type erasure while preserving behavioral equivalence. Contribution: We demonstrate that sequentiality is not intrinsic to the type layer, proposing a conceptually minimal paradigm for session typing. We prove that minimal session types are expressively complete, strongly type-safe, and guarantee behavioral equivalence—providing a simpler, more fundamental type foundation for verifying message-passing programs.

该论文通过引入独立性概念，利用可逆性研究进程演算中的并发、因果和冲突关系，并通过Beluga证明助手验证了相关理论。

This study addresses the lack of deductive reasoning foundations in discrete-event simulation, which hinders formal verification of model correctness and performance guarantees. To overcome this, we propose a core imperative calculus and proof system that extends reasoning over discrete-time probabilistic programs to performance models involving continuous time and distributions, rigorously establishing the soundness and completeness of the associated proof rules. Leveraging measure theory and the Lean theorem prover, we implement reasoning for almost-sure reachability and expected hitting times in continuous-time probabilistic programs. We successfully complete formal proofs on client-server architectures and network routing protocol case studies, thereby transcending the limitations of analytical solutions in classical queueing theory.

This work addresses the challenge of ensuring information-flow security when dynamically extending security lattices in concurrent systems. By extending an existing type system, it introduces—for the first time within the π-calculus—a scalable security lattice mechanism that supports runtime insertion of new security levels. The authors rigorously establish non-interference through reduction semantics and bisimulation equivalence. This approach overcomes the limitations of traditional static, binary security lattices by providing a formal verification framework that guarantees strict information isolation between high- and low-security levels, even as security policies are dynamically adjusted at runtime.

This work proposes λpitchfork, the first functional choreographic language supporting dynamic process spawning. Traditional concurrent programming requires separate programs for each participant, while existing choreographic approaches struggle to accommodate dynamic process creation. In contrast, λpitchfork enables runtime decisions about when, how, and with whom new processes are spawned, all while guaranteeing deadlock freedom. The language automatically generates distributed endpoint programs from a centralized choreographic specification. By integrating dynamic process spawning into functional choreographic programming, this approach rigorously combines theoretical soundness with practical expressiveness, effectively capturing real-world concurrency patterns such as load balancing and parallel divide-and-conquer. The correctness and practicality of λpitchfork are substantiated through formal verification and illustrative case studies.

This work addresses the challenge of correctly designing and verifying communication behaviors in complex interactive systems. It systematically traces the evolution of μCRL and its successor mCRL2, integrating process algebra, term rewriting systems, and modal μ-calculus to establish a formal modeling framework that combines rigorous mathematical foundations with practical engineering applicability. Building upon this foundation, the authors have developed a comprehensive mCRL2 toolset capable of modeling, automatically analyzing, and formally verifying the dynamic behavior of sophisticated computer-controlled systems. This integrated approach significantly enhances the scalability and usability of formal methods in real-world system design and validation.