Practical algorithms for MSO model-checking on tree-decomposable graphs

Langer, Alexander; Reidl, Felix; Rossmanith, Peter; Sikdar, Somnath

doi:10.1016/j.cosrev.2014.08.001

Cited by 27 publications

(32 citation statements)

References 150 publications

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“…To show that it is also tractable for graphs for which the treewidth is bounded by a constant, we will rely on a powerful result that is based on work of Courcelle, independently proved by Borie, Parker, and Tovey, and further extended by Arnborg, Lagergren, and Seese [3,14,16]. A survey by Langer et al [25] presents it in a slightly more general form than we require. For our purposes, the following will suffice:Theorem (see Theorem 30 of [25]) .…”

Section: Graphs With Constant‐bounded Treewidthmentioning

confidence: 99%

“…A survey by Langer et al [25] presents it in a slightly more general form than we require. For our purposes, the following will suffice:Theorem (see Theorem 30 of [25]) . Let G be a graph on n vertices , let w be a constant , and let

P

be a graph ‐ theoretic decision problem that can be expressed in the form of extended monadic second‐order logic.…”

Section: Graphs With Constant‐bounded Treewidthmentioning

confidence: 99%

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The firebreak problem

et al. 2020

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Suppose we have a network that is represented by a graph G. Potentially a fire (or other type of contagion) might erupt at some vertex of G. We are able to respond to this outbreak by establishing a firebreak at k other vertices of G, so that the fire cannot pass through these fortified vertices. The question that now arises is which k vertices will result in the greatest number of vertices being saved from the fire, assuming that the fire will spread to every vertex that is not fully behind the k vertices of the firebreak. This is the essence of the Firebreak decision problem, which is the focus of this paper. We establish that the problem is intractable on the class of split graphs as well as on the class of bipartite graphs, but can be solved in linear time when restricted to graphs having constant‐bounded treewidth, or in polynomial time when restricted to intersection graphs. We also consider some closely related problems.

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Section: Graphs With Constant‐bounded Treewidthmentioning

confidence: 99%

P

be a graph ‐ theoretic decision problem that can be expressed in the form of extended monadic second‐order logic.…”

Section: Graphs With Constant‐bounded Treewidthmentioning

confidence: 99%

The firebreak problem

et al. 2020

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“…checking whether a given program/contract satisfies a property specified in µ-calculus, but the problem can be solved in linear time if the CFG has constant treewidth [41]. Similarly, model checking MSO properties is NP-hard in general, but can be done in linear time if the underlying graph has constant treewidth [36].…”

Section: Motivating Examplesmentioning

confidence: 99%

“…Hence, there has been ample research on exploiting the structural properties of the underlying CFGs to obtain faster algorithms [3]. An extensively-studied parameter that has been applied successfully to these problems is the treewidth [8,13,16,32,36,41,47]. See section 2.3 for some motivating examples.…”

Section: Introductionmentioning

confidence: 99%

The treewidth of smart contracts

Chatterjee

Goharshady

2019

Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing

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Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money in the form of cryptocurrency units. Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can potentially cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed and verified by every node in the Blockchain network. Hence, optimizations in compiling smart contracts can lead to significant savings of computation, time and energy. Two classical approaches in both program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, optimization and analysis problems are often reduced to graph problems over the control flow graph (CFG) of the program. However, the resulting graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs to obtain efficient algorithms for these problems. One well-studied structural property is the treewidth. Treewidth is a measure of tree-likeness of graphs and small treewidth can be exploited for efficient algorithms. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. Bounded treewidth has been used as a basis for many efficient intraprocedural analyses. In this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case.

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“…There are other methods intended to overcome the "size problem" that is unavoidable with finite automata [28,38]. Kneis et al [33,36] use games in the following way. From a graph G given with a tree-decomposition T and an MS sentence ϕ to check, they build a model-checking game GpT, ϕq that is actually a tree.…”

Section: Alternative Toolsmentioning

confidence: 99%

Computations by fly-automata beyond monadic second-order logic

Courcelle

Durand

2016

Theoretical Computer Science

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The validity of a monadic-second order (MS) expressible property can be checked in linear time on graphs of bounded tree-width or clique-width given with appropriate decompositions. This result is proved by constructing from the MS sentence expressing the property and an integer that bounds the tree-width or clique-width of the input graph, a finite automaton intended to run bottom-up on the algebraic term representing a decomposition of the input graph. As we cannot construct practically the transition tables of these automata because they are huge, we use flyautomata whose states and transitions are computed "on the fly", only when needed for a particular input. Furthermore, we allow infinite sets of states and we equip automata with output functions. Thus, they can check properties that are not MS expressible and compute values, for an example, the number of p-colorings of a graph. We obtain XP and FPT graph algorithms, parameterized by tree-width or clique-width. We show how to construct easily such algorithms by combining predefined automata for basic functions and properties. These combinations reflect the structure of the MS formula that specifies the property to check or the function to compute.

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Practical algorithms for MSO model-checking on tree-decomposable graphs

Cited by 27 publications

References 150 publications

The firebreak problem

The firebreak problem

The treewidth of smart contracts

Computations by fly-automata beyond monadic second-order logic

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