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Tight bounds for reachability problems on one-counter and pushdown systems

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We consider the problem of reachability on One-Counter Systems (OCSs) and Pushdown Systems (PDSs). The problem has a well-known O(n3) bound on both models, while the bound is believed to be tight for PDSs. Here we establish new upper and lower bounds for reachability on OCSs and restricted PDSs. We show that the problem can be solved (i) in O(nω⋅log2⁡n) time on OCSs, and (ii) in O(n2) time on sparse PDSs when restricted to witness executions of stack height bounded by log⁡n. Moreover, we prove similar lower bounds.
Original languageEnglish
Article number106135
JournalInformation Processing Letters
Publication statusPublished - Oct 2021

    Research areas

  • Pushdown systems, One-counter systems, Dyck reachability, Formal languages

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