# Faster algorithms for quantitative verification in constant treewidth graphs

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs. CAV: Computer Aided Verification, LNCS, vol. 9206, 140–157.

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http://arxiv.org/abs/1504.07384
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LNCS

Abstract

We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m=O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of ϵ in time O(n⋅log(n/ϵ)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n⋅log(|a⋅b|))=O(n⋅log(n⋅W)), when the output is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2⋅m) time and the associated decision problem can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.

Publishing Year

Date Published

2015-07-16

Acknowledgement

The research was partly supported by Austrian Science Fund (FWF) Grant No P23499- N23, FWF NFN Grant No S11407-N23 (RiSE/SHiNE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.

Volume

9206

Page

140 - 157

Conference

CAV: Computer Aided Verification

Conference Location

San Francisco, CA, USA

Conference Date

2015-07-18 – 2015-07-24

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### Cite this

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Faster algorithms for quantitative verification in constant treewidth graphs. In: Vol 9206. Springer; 2015:140-157. doi:10.1007/978-3-319-21690-4_9

Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). Faster algorithms for quantitative verification in constant treewidth graphs (Vol. 9206, pp. 140–157). Presented at the CAV: Computer Aided Verification, San Francisco, CA, USA: Springer. https://doi.org/10.1007/978-3-319-21690-4_9

Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs,” 9206:140–57. Springer, 2015. https://doi.org/10.1007/978-3-319-21690-4_9.

K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Faster algorithms for quantitative verification in constant treewidth graphs,” presented at the CAV: Computer Aided Verification, San Francisco, CA, USA, 2015, vol. 9206, pp. 140–157.

Chatterjee, Krishnendu, et al.

*Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs*. Vol. 9206, Springer, 2015, pp. 140–57, doi:10.1007/978-3-319-21690-4_9.**All files available under the following license(s):**

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