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Preprints, Working Papers, ... (Preprint) Year : 2022

Algorithms and Hardness Results for Computing Cores of Markov Chains


Given a Markov chain M = (V, v0, δ), with state space V and a starting state v0, and a probability threshold , an-core is a subset C of states that is left with probability at most. More formally, C ⊆ V is an-core, iff P reach (V \C) ≤. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an-core of a given size is NP-complete. This solves an open problem posed in [26]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset.
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Dates and versions

hal-03808158 , version 1 (03-11-2022)


  • HAL Id : hal-03808158 , version 1


Ali Ahmadi, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, Roodabeh Safavi, et al.. Algorithms and Hardness Results for Computing Cores of Markov Chains. 2022. ⟨hal-03808158⟩


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