automata theory

This work addresses the challenges of model uncertainty and unpredictability in partially observable or black-box systems during runtime by proposing a unified theoretical framework that integrates epistemic logic with temporal logic. Leveraging automata theory, it systematically formalizes core concepts—including specification, diagnosis, opacity, and monitorability—and synthesizes lightweight online monitors through offline analysis. The approach is extended to real-time systems, resolving key issues related to their temporal semantics and algorithmic complexity. Furthermore, the study precisely characterizes the fundamental limits of runtime verification, thereby establishing a constructive and implementable foundation for practical deployment of monitoring mechanisms.

This paper investigates whether deterministic computation can be fully characterized by a finite algebraic system analogous to Kleene Algebra with Tests (KAT). Specifically, it addresses whether the deterministic fragment of KAT admits a finite set of control-flow operations sufficient to generate all deterministic finite-state computations. Method: Drawing on formal language theory, algebraic semantics, regular algebra, and model-theoretic techniques, the authors rigorously analyze the expressive limitations of finite algebraic signatures over deterministic automata. Contribution/Results: The paper establishes, for the first time, that no finite set of control-flow primitives can axiomatize the entire class of deterministic finite-state computations—thereby refuting the existence of a KAT-style complete algebraic framework for determinism. This result demonstrates an intrinsic incompleteness in the algebraic characterization of deterministic computation and reveals a fundamental expressiveness boundary of classical control structures (sequence, conditionals, loops), advancing foundational understanding of computational representability in program algebras.

Traditional binary correctness verification fails to capture quantitative system behaviors. Method: We propose the first automated toolkit for quantitative automata supporting six classical semantics—Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg—and systematically address core decision problems: emptiness, inclusion, equivalence, and safety/liveness verification. Our approach introduces weighted transition modeling and a generalized value-function framework, integrating symbolic decision procedures, optimization solvers, and automata transformation techniques to enable extremal-value computation, safety-liveness decomposition, and real-time monitoring. Contribution/Results: Experiments demonstrate efficiency on inclusion checking, constant-function recognition, and online monitoring tasks. We release the first open-source benchmark suite for quantitative automata analysis, establishing a scalable, modular, and unified infrastructure for quantitative system verification.

This paper addresses the lack of a unified formal framework for modeling operational semantics of programming languages and verifying program correctness. We propose a novel unifying framework based on multi-sorted hybrid modal logic—the first application of such a logic to operational semantics modeling—significantly reducing representational distance in semantic encoding. Compared with dynamic logic, our approach more naturally captures program execution dynamics; relative to traditional weakest precondition calculi, it offers superior expressiveness and semantic clarity. The framework uniformly supports semantic definition, property specification, and formal verification. Crucially, we establish key completeness results, thereby laying a theoretically rigorous foundation that retains practical expressivity for formal program verification.

Automated verification of interactive console I/O programs in Haskell education remains challenging due to the dynamic, history-dependent nature of student implementations. Method: We propose a lightweight, formal behavioral specification language that uniquely integrates global state and execution history, expressed via regex-like syntax; its trace-based semantics enable probabilistic testing and scalable verification through *sampleable validity*. Contribution/Results: Our system automatically validates student submissions against behavioral specifications and supports pedagogical closed-loop applications—including real-time feedback generation, example solution synthesis, and exercise randomization. Empirical evaluation demonstrates substantial improvements in test coverage and pedagogical adaptability while preserving formal rigor. To our knowledge, this is the first framework for verifying interactive behaviors in functional programming education that simultaneously achieves theoretical soundness and practical deployability.

Existing systems lack mechanisms to effectively verify at compile time whether sensitive data is used in accordance with its intended purposes. This work proposes a typestate-based approach that models the typestate of sensitive data as the set of its permitted uses and supports dynamic adjustments under runtime changes in data usage, thereby enabling static enforcement of purpose compliance. As the first effort to apply typestate to data purpose verification, we design and implement PurPL, an object-oriented language featuring a purpose-aware type system that provides strong compile-time guarantees. Experimental evaluation demonstrates that our approach is both effective and practical across a range of sensitive data processing scenarios.

This work proposes the first model checking approach for CTL* temporal logic tailored to infinite families of finite-state transition systems generated by highly configurable systems or software product lines. The method employs context-free graph grammars to uniformly model the entire system family and introduces a grammar-rule-based, compositional state labeling algorithm. This algorithm recursively propagates state labels using only finite contextual information, enabling the verification of whether all, some, or infinitely many members of the family satisfy a given CTL* property. Experimental results demonstrate that the approach effectively supports unified formal verification across infinite system families, offering a scalable solution for reasoning about complex configurable systems within a rigorous logical framework.

This work addresses the formal semantics of governed program execution by proposing the first algebraic framework whose expressiveness is strictly aligned with governance boundaries. Building upon interaction trees and parameterized coinduction, the authors define a governance algebra axiomatized by safety, transparency, and propriety, which induces a symmetric monoidal category structure preserving governance properties. An algebraic effect system combined with capability-indexed types ensures that governance and capability constraints hold simultaneously under all compositions. The development is formally verified in Coq, comprising 454 theorems (12,000 lines of code), and extracted into an OCaml runtime validated on the BEAM virtual machine against over 70,000 test cases. The system retains Turing completeness while excluding unmediated I/O, modeling governance denial as safe coinductive divergence.

This work addresses the challenge of linear temporal logic (LTL) model checking for infinite-state systems by introducing the MoAT framework, which innovatively reduces LTL verification to a fair termination problem. By leveraging existing termination analysis tools—KoAT and LoAT—the approach enables efficient solving of the reduced problem. MoAT uniquely integrates automata-theoretic techniques with fair termination reductions, representing the first systematic application of termination analyzers to LTL model checking. Experimental evaluation demonstrates that MoAT achieves performance on par with state-of-the-art tools for LTL verification over infinite-state systems.