2026-07-23T04:27:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17421 2024-03-06T10:59:42Z ddc:004 open_access

Algorithms and Hardness Results for Computing Cores of Markov Chains Ahmadi, Ali Chatterjee, Krishnendu Goharshady, Amir Kafshdar Meggendorfer, Tobias Safavi, Roodabeh Žikelić, Ðorđe Markov Chains Cores Complexity Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, 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 [Jan Kretínský and Tobias Meggendorfer, 2020]. 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ali Ahmadi and Krishnendu Chatterjee and Amir Kafshdar Goharshady and Tobias Meggendorfer and Roodabeh Safavi and Ðorđe Žikelić 2022 Is Part Of LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2022.29 urn:nbn:de:0030-drops-174216 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.29 eng https://creativecommons.org/licenses/by/4.0/legalcode