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An efficient simulation algorithm on Kripke structures

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Abstract

A number of algorithms for computing the simulation preorder (and equivalence) on Kripke structures are available. Let \(\varSigma \) denote the state space, \({\rightarrow }\) the transition relation and \(P_{\mathrm {sim}}\) the partition of \(\varSigma \) induced by simulation equivalence. While some algorithms are designed to reach the best space bounds, whose dominating additive term is \(|P_{\mathrm {sim}}|^2\), other algorithms are devised to attain the best time complexity \(O(|P_{\mathrm {sim}}||{\rightarrow }|)\). We present a novel simulation algorithm which is both space and time efficient: it runs in \(O(|P_ {\mathrm {sim}}|^2 \log |P_{\mathrm {sim}}| + |\varSigma |\log |\varSigma |)\) space and \(O(|P_{\mathrm {sim}}||{\rightarrow }|\log |\varSigma |)\) time. Our simulation algorithm thus reaches the best space bounds while closely approaching the best time complexity.

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Acknowledgments

We acknowledge the contribution of Francesco Tapparo to a preliminary stage of this research which was informally presented in [27]. This work was partially supported by Microsoft Research SEIF 2013 Award and by the University of Padova under the project BECOM.

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  1. Dipartimento di Matematica, University of Padova, Padova, Italy

    Francesco Ranzato

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  1. Francesco Ranzato
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Correspondence to Francesco Ranzato.

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Ranzato, F. An efficient simulation algorithm on Kripke structures. Acta Informatica 51, 107–125 (2014). https://doi.org/10.1007/s00236-014-0195-9

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  • DOI: https://doi.org/10.1007/s00236-014-0195-9

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