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arXiv 1402.2698cs.LOcs.DCcs.DS
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基于MSO逻辑的并发系统的自动验证、综合与校正

Automated Verification, Synthesis and Correction of Concurrent Systems via MSO Logic

Mateus de Oliveira Oliveira

摘要:

在这项工作中,我们提供了算法解决方案的五个基本问题的验证,合成和校正的并发系统,可以建模有界p/t-网。我们表示并发通过偏序,并假设行为规范通过一元二阶逻辑。c-偏序是Hasse图可以被c路覆盖的偏序。对于有限的变迁集T,设P(c,T,n)表示所有T-标号的c-偏序满足n的集合。若N=(P,T)是p/t-网,则P(N,c)表示N的所有c-偏序游程的集合。一个(b,r)-有界p/t-网是一个b-有界p/t-网,其中每个位置最多重复出现r次。我们解决了以下问题:1.验证:给定一个MSO公式n和一个有界p/t网N,确定P(N,c)是否\subseteq P(c,T,n),P(c,T,n)是否\subseteq P(N,c),或P(N,c)\cap P(c,T,n)是否= \emptyset。2.根据MSO质量标准合成:给定一个MSO公式n,合成一个满足P(c,T,n)\subseteq P(N,c)的语义极小(b,r)-有界p/t-网N. 3.语义最安全子系统:给定一个定义安全偏序集的MSO公式,和一个可能包含不安全行为的b-有界p/t-net N,合成出行为介于P(N,c)\cap P(c,T,N)和P(N,c)之间的最安全的(b,r)-有界p/t-net N'. 4.行为修复:给定两个MSO公式\cap P(c,T,)和一个b-有界p/t-网N,合成一个语义极小(b,r)-有界p/t网N',其行为介于P(N,c)和P(c,T,)之间. 5.合同综合:给定指定一组好行为的MSO公式^yes和指定一组坏行为的MSO公式^no,合成一个语义上最小的(b,r)-有界p/t-网N,使得P(c,T,^yes)\subseteq P(N,c)但P(c,T,^no)\cap P(N,c)= \emptyset。

英文摘要:

In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and assume that behavioral specifications are given via monadic second order logic. A c-partial-order is a partial order whose Hasse diagram can be covered by c paths. For a finite set T of transitions, we let P(c,T,ϕ) denote the set of all T-labelled c-partial-orders satisfying ϕ. If N=(P,T) is a p/t-net we let P(N,c) denote the set of all c-partially-ordered runs of N. A (b, r)-bounded p/t-net is a b-bounded p/t-net in which each place appears repeated at most r times. We solve the following problems: 1. Verification: given an MSO formula ϕand a bounded p/t-net N determine whether P(N,c)\subseteq P(c,T,ϕ), whether P(c,T,ϕ)\subseteq P(N,c), or whether P(N,c)\cap P(c,T,ϕ)=\emptyset. 2. Synthesis from MSO Specifications: given an MSO formula ϕ, synthesize a semantically minimal (b,r)-bounded p/t-net N satisfying P(c,T,ϕ)\subseteq P(N, c). 3. Semantically Safest Subsystem: given an MSO formula ϕdefining a set of safe partial orders, and a b-bounded p/t-net N, possibly containing unsafe behaviors, synthesize the safest (b,r)-bounded p/t-net N' whose behavior lies in between P(N,c)\cap P(c,T,ϕ) and P(N,c). 4. Behavioral Repair: given two MSO formulas ϕand ψ, and a b-bounded p/t-net N, synthesize a semantically minimal (b,r)-bounded p/t net N' whose behavior lies in between P(N,c) \cap P(c,T,ϕ) and P(c,T,ψ). 5. Synthesis from Contracts: given an MSO formula ϕ^yes specifying a set of good behaviors and an MSO formula ϕ^no specifying a set of bad behaviors, synthesize a semantically minimal (b,r)-bounded p/t-net N such that P(c,T,ϕ^yes) \subseteq P(N,c) but P(c,T,ϕ^no ) \cap P(N,c)=\emptyset.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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