Parametrized Universality Problems for One-Counter Nets



Almagor, Shaull, Boker, Udi, Hofman, Piotr and Totzke, Patrick ORCID: 0000-0001-5274-8190
(2020) Parametrized Universality Problems for One-Counter Nets. .

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Abstract

We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in both parameters. This yields two natural questions: 1) Does there exist an initial counter value that makes the language universal? 2) Does there exist a sufficiently high ceiling so that the bounded language is universal? Although the ordinary universality problem is decidable (and Ackermann-complete) and these parameterized problems seem to reduce to checking basic structural properties of the underlying automaton, we show that in fact both problems are undecidable. We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: cs.FL, cs.FL
Depositing User: Symplectic Admin
Date Deposited: 01 Sep 2020 09:12
Last Modified: 14 Oct 2021 12:05
Open Access URL: https://drops.dagstuhl.de/opus/frontdoor.php?sourc...
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3099166