Efficient Computation of Inductive Invariants for Regular Abstraction Frameworks

Alapfogalmak

The paper introduces regular abstraction frameworks, a generalization of the approach to regular model checking based on inductive invariants. It shows that the problem of deciding if the language of the automaton recognizing an overapproximation of the reachable configurations intersects a given regular set of unsafe configurations is EXPSPACE-complete. The paper also presents a learning algorithm that computes this automaton in a lazy manner, stopping whenever the current hypothesis is already strong enough to prove safety.

Kivonat

The paper introduces regular abstraction frameworks, a generalization of the approach to regular model checking based on inductive invariants. Regular abstraction frameworks consist of a regular language of constraints and an interpretation that assigns to each constraint the set of configurations of the regular transition system (RTS) satisfying it. Examples of regular abstraction frameworks include the formulas of previous work, octagons, bounded difference matrices, and views.

The paper shows that the generalization of the decision problem to regular abstraction frameworks remains in EXPSPACE, and proves a matching EXPSPACE-hardness bound. This implies that, in the worst case, the automaton recognizing the overapproximation of the reachable configurations has a double-exponential number of states.

To address this, the paper introduces a learning algorithm that computes this automaton in a lazy manner, stopping whenever the current hypothesis is already strong enough to prove safety. The algorithm involves solving the separability problem: given a pair of configurations, is there an inductive constraint that separates them? The paper shows that this problem is PSPACE-complete and NP-complete for length-preserving interpretations.

The experimental results show that the learning-based approach outperforms the previous approach.

Statisztikák

The paper does not provide any specific numerical data or statistics. It focuses on theoretical results regarding the complexity of the abstract safety problem and the design of a learning-based algorithm.

Idézetek

"Regular transition systems (RTS) are a popular formalism for modelling infinite-state systems satisfying the following conditions: configurations can be encoded as words, the set of initial configurations is recognised by a finite automaton, and the transition relation is recognised by a transducer."
"Regular abstraction frameworks are a formalism to model a wide range of abstractions. An abstraction framework is a triple F = (C, A, V), where C is a set of configurations, A is a set of constraints, and V ⊆A × C is an interpretation."
"EXPSPACE-hardness implies that, in the worst case, the automaton recognising the overapproximation of the reachable configurations has a double-exponential number of states."

Főbb Kivonatok

Computing Inductive Invariants of Regular Abstraction Frameworks

by Philipp Czer... : arxiv.org 04-17-2024

https://arxiv.org/pdf/2404.10752.pdf

Mélyebb kérdések

How can the learning algorithm be extended to handle more expressive constraint languages beyond regular languages

To extend the learning algorithm to handle more expressive constraint languages beyond regular languages, we can incorporate techniques from automata learning and formal language theory. One approach could be to utilize techniques from learning theory, such as active learning algorithms, to efficiently learn more complex constraint languages. By adapting algorithms that can handle non-regular languages, such as probabilistic automata or tree automata, we can enhance the expressiveness of the learned constraints. Additionally, incorporating techniques from machine learning, such as neural networks or deep learning, could provide a way to learn and represent more intricate constraint languages. By combining these advanced learning methods with the existing framework, we can extend the algorithm to handle a wider range of constraint languages.

What are the potential applications of regular abstraction frameworks beyond the verification of regular transition systems

Regular abstraction frameworks have various potential applications beyond the verification of regular transition systems. One application is in the field of program analysis and verification, where regular abstractions can be used to model and analyze complex software systems. By abstracting the behavior of programs into regular constraints, it becomes possible to verify properties of the software, such as correctness, safety, and security. Regular abstraction frameworks can also be applied in the domain of natural language processing, where they can be used to model and analyze linguistic structures and patterns. By representing language constraints using regular abstractions, tasks such as text processing, information extraction, and sentiment analysis can be efficiently performed. Additionally, regular abstraction frameworks can be utilized in the field of bioinformatics to model biological sequences and analyze genetic data. By applying regular abstractions to genomic sequences, protein structures, and biological networks, researchers can gain insights into complex biological systems and processes.

Can the techniques developed in this paper be applied to other classes of infinite-state systems beyond regular transition systems

The techniques developed in the paper can be applied to other classes of infinite-state systems beyond regular transition systems. One potential application is in the verification of parameterized systems with infinite state spaces, such as concurrent programs or distributed systems. By extending the regular abstraction frameworks to model and analyze parameterized systems, it becomes possible to verify properties of these systems, such as deadlock freedom, liveness, and fairness. The learning algorithm can be adapted to handle the complexities of parameterized systems and provide insights into their behavior. Additionally, the techniques can be applied to infinite-state models in formal methods, such as infinite-state automata or infinite-state Markov chains, to analyze probabilistic systems and temporal properties. By leveraging the power of regular abstraction frameworks and automata learning, researchers can tackle a wide range of infinite-state systems and verify critical properties in various domains.