Search arXivSearch

arXiv · 2408.03488

Recomposition: A New Technique for Efficient Compositional Verification

Abstract

Compositional verification algorithms are well-studied in the context of model checking. Properly selecting components for verification is important for efficiency, yet has received comparatively less attention. In this paper, we address this gap with a novel compositional verification framework that focuses on component selection as an explicit, first-class concept. The framework decomposes a system into components, which we then recompose into new components for efficient verification. At the heart of our technique is the recomposition map that determines how recomposition is performed; the component selection problem thus reduces to finding a good recomposition map. However, the space of possible recomposition maps can be large. We therefore propose heuristics to find a small portfolio of recomposition maps, which we then run in parallel. We implemented our techniques in a model checker for the TLA+ language. In our experiments, we show that our tool achieves competitive performance with TLC-a well-known model checker for TLA+-on a benchmark suite of distributed protocols.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ian Dardik, April Porter, Eunsuk Kang. 2024-08-15. Recomposition: A New Technique for Efficient Compositional Verification. https://arxiv.org/abs/2408.03488

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

A Myhill-Nerode Theorem for Generalized Automata, with Applications to Pattern Matching and Compression

The model of generalized automata, introduced by Eilenberg in 1974, allows representing a regular language more concisely than conventional automata by allowing edges to be labeled not only with characters, but also strings. Giammarresi and Montalbano introduced a notion of determinism for generalized automata [STACS 1995]. While generalized deterministic automata retain many properties of conventional deterministic automata, the uniqueness of a minimal generalized deterministic automaton is lost. In the first part of the paper, we show that the lack of uniqueness can be explained by introducing a set $ \mathcal{W(A)} $ associated with a generalized automaton $ \mathcal{A} $. In this way, we derive for the first time a full Myhill-Nerode theorem for generalized automata, which contains the textbook Myhill-Nerode theorem for conventional automata as a degenerate case. In the second part of the paper, we show that the set $ \mathcal{W(A)} $ leads to applications for pattern matching and data compression. We show that a Wheeler generalized automata can be stored using $ \mathfrak{e} \log σ(1 + o(1)) + O(e) $ bits so that pattern matching queries can be solved in $ O(m \log \log σ) $ time, where $ \mathfrak{e} $ is the total length of all edge labels, $ e $ is the number of edges, $ σ$ is the size of the alphabet and $ m $ is the length of the pattern.

cs.FL

Quadratic Word Equations with a Linear Side: Polynomial Nielsen Graph Diameter and NP-Completeness

The satisfiability problem for word equations asks whether variables can be replaced by words so that the two sides become equal. For regular word equations, in which each variable occurs at most once on each side, satisfiability is NP-complete. For general quadratic word equations, in which each variable occurs at most twice in total, satisfiability is NP-hard, but its membership in NP remains open. We consider an intermediate class: quadratic word equations with a linear side, where each variable occurs at most once on one designated side. We show that the Nielsen graph of an equation $U=V$ in this class, with total length $N=|U|+|V|$, has diameter $O(N^{12})$, measured over reachable pairs of vertices. Together with the known NP-hardness for regular word equations, this result establishes NP-completeness of satisfiability for this class. We also show that each strongly connected component is isomorphic to the length-preserving reachability graph of a regular equation, and that the condensation graph has depth at most $|U|+2|V|$.

cs.FL

Contributions to the hierarchy of probabilistic languages

We reconsider the theory of probabilistic formal languages generated by n-gram models and by probabilistic context-free grammars (PCFGs). The expected hierarchy of probabilistic grammars is established by proving that every probabilistic language generated by an n-gram model is also generated by some PCFG, while some probabilistic languages generated by PCFGs cannot be generated by any $n$-gram model. We introduce the notion of fully connected PCFGs, namely PCFGs in Chomsky normal form where every production rule only involving non-terminals has non-zero probability. Our main result shows that any probabilistic language generated by an $n$-gram model differs from any probabilistic language generated by a fully connected PCFG. Therefore, the class of probabilistic languages generated by $n$-gram models is not a subset of the class generated by fully connected PCFGs.

cs.FL