Lowerbounds for Bisimulation by Partition Refinement

IF 0.6 4区 数学 Q4 COMPUTER SCIENCE, THEORY & METHODS
Jan Friso Groote, Jan Martens, Erik. P. de Vink
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引用次数: 0

Abstract

We provide time lower bounds for sequential and parallel algorithms deciding bisimulation on labeled transition systems that use partition refinement. For sequential algorithms this is $\Omega((m \mkern1mu {+} \mkern1mu n ) \mkern-1mu \log \mkern-1mu n)$ and for parallel algorithms this is $\Omega(n)$, where $n$ is the number of states and $m$ is the number of transitions. The lowerbounds are obtained by analysing families of deterministic transition systems, ultimately with two actions in the sequential case, and one action for parallel algorithms. For deterministic transition systems with one action, bisimilarity can be decided sequentially with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that this approach is not of help to develop a faster generic algorithm for deciding bisimilarity. For parallel algorithms there is a similar situation where these techniques may be applied, too.
分区细化双仿真的下限
我们提供了时序和并行算法的时间下界,这些算法决定了使用分区细化的标记转移系统的双仿真。对于顺序算法,这是$\Omega((m \mkern1mu {+} \mkern1mu n ) \mkern-1mu \log \mkern-1mu n)$,对于并行算法,这是$\Omega(n)$,其中$n$是状态数,$m$是转换数。通过分析确定性过渡系统族得到了下限,最终在顺序情况下具有两个动作,而在并行算法中具有一个动作。对于具有一个动作的确定性转换系统,可以使用与划分细化根本不同的技术来顺序确定双相似性。特别地,Paige, Tarjan和Bonic给出了一个针对这种特殊情况的线性算法。我们利用oracle的概念表明,这种方法无助于开发用于确定双相似性的更快的通用算法。对于并行算法,也有类似的情况可以应用这些技术。
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来源期刊
Logical Methods in Computer Science
Logical Methods in Computer Science 工程技术-计算机:理论方法
CiteScore
1.80
自引率
0.00%
发文量
105
审稿时长
6-12 weeks
期刊介绍: Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.
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