Faster algorithms for quantitative verification in constant treewidth graphs
IST Austria Technical Report
Chatterjee, Krishnendu
Ibsen-Jensen, Rasmus
Pavlogiannis, Andreas
ddc:000
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 mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) 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 · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
IST Austria
2015
info:eu-repo/semantics/other
doc-type:other
text
http://purl.org/coar/resource_type/c_1843
https://research-explorer.ista.ac.at/record/5430
https://research-explorer.ista.ac.at/download/5430/5482
Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. <i>Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs</i>. IST Austria; 2015. doi:<a href="https://doi.org/10.15479/AT:IST-2015-319-v1-1">10.15479/AT:IST-2015-319-v1-1</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.15479/AT:IST-2015-319-v1-1
info:eu-repo/semantics/altIdentifier/issn/2664-1690
info:eu-repo/semantics/openAccess