The geometry of reachability in continuous vector addition systems with states

IF 0.8 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Shaull Almagor , Arka Ghosh , Tim Leys , Guillermo A. Pérez
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引用次数: 0

Abstract

We study the geometry of reachability sets of continuous vector addition systems with states (VASS). In particular we establish that they are “almost” Minkowski sums of convex cones and zonotopes generated by the vectors labelling the transitions of the VASS. We use the latter to prove that short so-called linear path schemes suffice as witnesses of reachability in continuous VASS. Then, we give new polynomial-time algorithms for the reachability problem for linear path schemes. Finally, we also establish that enriching the model with zero tests makes the reachability problem intractable already for linear path schemes of dimension two.

Abstract Image

带状态的连续向量相加系统的可达性几何
研究了带状态连续向量相加系统(VASS)的可达集的几何性质。特别地,我们确定它们是凸锥和带形的“几乎”闵可夫斯基和,这些和是由标记VASS过渡的向量产生的。我们使用后者来证明短的所谓线性路径方案足以作为连续VASS的可达性的见证。然后,给出了求解线性路径可达性问题的新的多项式时间算法。最后,我们还证明了用零检验来丰富模型使得二维线性路径格式的可达性问题已经难以解决。
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来源期刊
Information and Computation
Information and Computation 工程技术-计算机:理论方法
CiteScore
2.30
自引率
0.00%
发文量
119
审稿时长
140 days
期刊介绍: Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking
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