Deciding Polynomial Termination Complexity for VASS Programs

02/13/2021 ∙ by Michal Ajdarów, et al. ∙ 0

We show that for every fixed k≥ 3, the problem whether the termination/counter complexity of a given demonic VASS is 𝒪(n^k), Ω(n^k), and Θ(n^k) is coNP-complete, NP-complete, and DP-complete, respectively. We also classify the complexity of these problems for k≤ 2. This shows that the polynomial-time algorithm designed for strongly connected demonic VASS in previous works cannot be extended to the general case. Then, we prove that the same problems for VASS games are PSPACE-complete. Again, we classify the complexity also for k≤ 2. Interestingly, tractable subclasses of demonic VASS and VASS games are obtained by bounding certain structural parameters, which opens the way to applications in program analysis despite the presented lower complexity bounds.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 3

page 5

page 11

page 15

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.