中国科学院软件研究所机构知识库
Advanced  
ISCAS OpenIR  > 软件所图书馆  > 期刊论文
Title:
Rabin's theorem in the concurrency setting: A conjecture
Author: Thiagarajan, P.S. (1) ; Yang, Shaofa (2)
Corresponding Author: Thiagarajan, P.S.
Keyword: Rabin's theorem ; Monadic second order logic ; Event structure ; Petri net ; Grid-free
Source: Theoretical Computer Science
Issued Date: 2014
Volume: 546, Pages:225-236
Indexed Type: SCI ; EI
Department: (1) School of Computing, National University of Singapore, Singapore; (2) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, China
Abstract: Rabin's theorem says that the monadic second order theory of the infinite binary tree is decidable. This result has had a far reaching influence in the theory of branching time temporal logics. A simple consequence of Rabin's theorem is that for every finite state transition system, the monadic second order theory of its computation tree is decidable. Concurrency theory strongly suggests that finite 1-safe Petri nets (or simply, net systems) are a natural generalization of the notion of a finite state transition system while labelled event structures arising as the unfoldings of net systems are the proper counterparts to the computation trees obtained by unwinding finite (sequential) transition systems. It is easy to define the monadic second order theory of such event structures. It turns out that unlike the sequential case, not every net system (i.e. its event structure unfolding) has a decidable monadic second order theory. This gives rise to the question: Which net systems admit a decidable monadic second order theory? Here we present a conjecture based on a property called grid-freeness. Our conjecture is that a net system has a decidable monadic second order theory iff its event structure unfolding is grid-free. We show that it is decidable whether a net system has this property. We also prove that the monadic second order theory of a net system is undecidable if its event structure unfolding is not grid-free. In addition we show that our conjecture can be effectively reduced to the sub-class of free choice net systems. Finally we point out how the positive resolution of our conjecture will settle the decidability of a range of distributed controller synthesis problems.
English Abstract: Rabin's theorem says that the monadic second order theory of the infinite binary tree is decidable. This result has had a far reaching influence in the theory of branching time temporal logics. A simple consequence of Rabin's theorem is that for every finite state transition system, the monadic second order theory of its computation tree is decidable. Concurrency theory strongly suggests that finite 1-safe Petri nets (or simply, net systems) are a natural generalization of the notion of a finite state transition system while labelled event structures arising as the unfoldings of net systems are the proper counterparts to the computation trees obtained by unwinding finite (sequential) transition systems. It is easy to define the monadic second order theory of such event structures. It turns out that unlike the sequential case, not every net system (i.e. its event structure unfolding) has a decidable monadic second order theory. This gives rise to the question: Which net systems admit a decidable monadic second order theory? Here we present a conjecture based on a property called grid-freeness. Our conjecture is that a net system has a decidable monadic second order theory iff its event structure unfolding is grid-free. We show that it is decidable whether a net system has this property. We also prove that the monadic second order theory of a net system is undecidable if its event structure unfolding is not grid-free. In addition we show that our conjecture can be effectively reduced to the sub-class of free choice net systems. Finally we point out how the positive resolution of our conjecture will settle the decidability of a range of distributed controller synthesis problems.
Language: 英语
WOS ID: WOS:000340691500018
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16836
Appears in Collections:软件所图书馆_期刊论文

Files in This Item:

There are no files associated with this item.


Recommended Citation:
Thiagarajan, P.S. ,Yang, Shaofa . Rabin's theorem in the concurrency setting: A conjecture[J]. Theoretical Computer Science,2014-01-01,546:225-236.
Service
Recommend this item
Sava as my favorate item
Show this item's statistics
Export Endnote File
Google Scholar
Similar articles in Google Scholar
[Thiagarajan, P.S. (1)]'s Articles
[Yang, Shaofa (2)]'s Articles
CSDL cross search
Similar articles in CSDL Cross Search
[Thiagarajan, P.S. (1)]‘s Articles
[Yang, Shaofa (2)]‘s Articles
Related Copyright Policies
Null
Social Bookmarking
Add to CiteULike Add to Connotea Add to Del.icio.us Add to Digg Add to Reddit
所有评论 (0)
暂无评论
 
评注功能仅针对注册用户开放,请您登录
您对该条目有什么异议,请填写以下表单,管理员会尽快联系您。
内 容:
Email:  *
单位:
验证码:   刷新
您在IR的使用过程中有什么好的想法或者建议可以反馈给我们。
标 题:
 *
内 容:
Email:  *
验证码:   刷新

Items in IR are protected by copyright, with all rights reserved, unless otherwise indicated.

 

 

Valid XHTML 1.0!
Copyright © 2007-2019  中国科学院软件研究所 - Feedback
Powered by CSpace