{"paper":{"title":"The Odds of Staying on Budget","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LO"],"primary_cat":"cs.CC","authors_text":"Christoph Haase, Stefan Kiefer","submitted_at":"2014-09-21T17:49:56Z","abstract_excerpt":"Given Markov chains and Markov decision processes (MDPs) whose transitions are labelled with non-negative integer costs, we study the computational complexity of deciding whether the probability of paths whose accumulated cost satisfies a Boolean combination of inequalities exceeds a given threshold. For acyclic Markov chains, we show that this problem is PP-complete, whereas it is hard for the PosSLP problem and in PSPACE for general Markov chains. Moreover, for acyclic and general MDPs, we prove PSPACE- and EXP-completeness, respectively. Our results have direct implications on the complexit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8228","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}