Algorithms and Hardness Results for Computing Cores of Markov Chains.

Ahmadi, Ali and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Safavi, Roodabeh and Zikelic, Ðorde (2022) Algorithms and Hardness Results for Computing Cores of Markov Chains. In: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022 :. Leibniz International Proceedings in Informatics, LIPIcs . UNSPECIFIED, 29:1-29:20. ISBN 9783959772617

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Abstract

Given a Markov chain M = (V, v0, δ), with state space V and a starting state v0, and a probability threshold ϵ, an ϵ-core is a subset C of states that is left with probability at most ϵ. More formally, C ⊆ V is an ϵ-core, iff P [reach (V \C)] ≤ ϵ. 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 ϵ-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 ϵ-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 ϵ-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.

Item Type:
Contribution in Book/Report/Proceedings
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1700/1712
Subjects:
?? complexitycoresmarkov chainssoftware ??
ID Code:
213824
Deposited By:
Deposited On:
26 Feb 2024 14:55
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 05:25