微信服务号

微信订阅号

2025年4月7日 0:14 星期一
首页 > 过刊浏览>2018年第29卷第10期 >3009-3020. DOI:10.13328/j.cnki.jos.005321
PDF HTML阅读 XML下载 导出引用 引用提醒
良结构下推系统的可覆盖性问题的下界
作者:
作者简介:

李春淼(1993-),女,陕西商洛人,硕士,主要研究领域为形式化方法,程序语言理论;蔡小娟(1982-),女,博士,助理研究员,主要研究领域为形式化方法,程序语言理论;李国强(1979-),男,博士,副教授,CCF专业会员,主要研究领域为形式化方法,理论计算机科学,程序语言理论.

通讯作者:

李国强,E-mail:li.g@sjtu.edu.cn

基金项目:

国家自然科学基金（61472238，61672340，61872232）


Lower Bound for Coverability Problem of Well-Structured Pushdown Systems
Author:
Fund Project:

National Natural Science Foundation of China (61472238, 61672340, 61472240, 61872232)

  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献 [23]
    • |
  • 相似文献 [20]
    • | | |
  • 文章评论
    摘要:

    良结构下推系统是下推系统和良结构迁移系统的结合，该系统允许状态和栈字符是向量的形式，因而它们是无限的.状态迁移的同时允许栈进行入栈出栈的操作.它"非常接近不可判定的边缘".利用重置0操作，提出了一种模型可覆盖性问题复杂度下界的一般性证明方法，并且证明了状态是三维向量的子集和一般性的良结构下推系统的可覆盖性问题分别是Tower难和Hyper-Ackermann难的.

    Abstract:

    Well-Structured pushdown systems (WSPDSs) combine pushdown systems and well-structured transition systems to allow locations and stack alphabets to be vectors, and thus they are unbounded. States change with the push and pop operations on the stack. The model has been said to be "very close to the border of undecidability". This paper proposes a general framework to get the lower bounds for coverability complexity of a model by adopting the reset-zero method. The paper proves that the complexity is Tower-hard when a WSPDS is restricted with three dimensional state vectors, and Hyper-Ackermann hard for the general WSPDSs.

    参考文献
    [1] Derick WD. Theory of Computation:A Primer. Boston:Addison-Wesley Longman Publishing Co., 1987.
    [2] Autebert JM, Berstel J, Boasson L. Context-Free languages and pushdown automata. Handbook of Formal Languages, 1997,6(3):111-174.[doi:10.1007/978-3-642-59136-5_3]
    [3] Abdulla PA, Čerāns K, Jonsson B, Tsay YK. Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation, 2000,160(1-2):109-127.[doi:10.1006/inco.1999.2843]
    [4] Cai X, Ogawa M. Well-Structured pushdown systems. In:D'Argenio PR, Melgratti H, eds. Proc. of the Int'l Conf. on Concurrency Theory. Berlin:Springer-Verlag, 2013. 121-136.[doi:10.1007/978-3-642-40184-8_10]
    [5] Jin Y, Cai XJ, Li GQ. Expressiveness of well-structured pushdown systems. Journal of Shanghai Jiaotong University, 2015,49(8):1084-1089(in Chinese with English abstract).[doi:10.16183/j.cnki.jsjtu.2015.08.002]
    [6] Leroux J, Praveen M, Sutre G. Hyper-Ackermannian bounds for pushdown vector addition systems. In:Henzinger T, Miller D, eds. Proc. of the Joint Meeting of the 23rd EACSL Annual Conf. on Computer Science Logic (CSL) and the 29th Annual ACM/IEEE Symp. on Logic in Computer Science (LICS). New York:ACM, 2014. Article 63.[doi:10.1145/2603088.2603146]
    [7] Sen K, Viswanathan M. Model checking multithreaded programs with asynchronous atomic methods. In:Ball T, Jones RB, eds. Proc. of the Int'l Conf. on Computer Aided Verification. Berlin:Springer-Verlag, 2006. 300-314.[doi:10.1007/11817963_29]
    [8] Kochems J, Luke Ong CH. Safety verification of asynchronous pushdown systems with shaped stacks. In:D'Argenio PR, Melgratti H, eds. Proc. of the Int'l Conf. on Concurrency Theory. Berlin:Springer-Verlag, 2013. 288-302.[doi:10.1007/978-3-642-40184-8_21]
    [9] Bouajjani A, Emmi M. Analysis of recursively parallel programs. In:Field J, ed. Proc. of the 39th Annual ACM SIGPLANSIGACT Symp. on Principles of Programming Languages. New York:ACM, 2012. 203-214.[doi:10.1145/2103621.2103681]
    [10] Lipton RJ. The reachability problem requires exponential space[Ph.D. Thesis]. Department of Computer Science, Yale University, 1976.
    [11] Lazic R. The reachability problem for vector addition systems with a stack is not elementary. Computer Science, 2013.
    [12] Schnoebelen P. Revisiting Ackermann-Hardness for lossy counter machines and reset Petri nets. Lecture Notes in Computer Science, 2010,6281:616-628.[doi:10.1007/978-3-642-15155-2_54]
    [13] Haddad S, Schmitz S, Schnoebelen P. The ordinal-recursive complexity of timed-arc Petri nets, data nets, and other enriched nets. In:Logic in Computer Science. IEEE, 2012. 355-364.[doi:10.1109/LICS.2012.46]
    [14] Demri S, Jurdziński M, Lachish O, Lazić R. The covering and boundedness problems for branching vector addition systems. Journal of Computer and System Sciences, 2013,79(1):23-38.[doi:10.1016/j.jcss.2012.04.002]
    [15] Lazić R. The reachability problem for branching vector addition systems requires doubly-exponential space. Information Processing Letters, 2010,110(17):740-745.[doi:10.1016/j.ipl.2010.06.008]
    [16] Bonnet R. The reachability problem for vector addition system with one zero-test. In:Murlak F, Sankowski P, eds. Mathematical Foundations of Computer Science. Berlin:Springer-Verlag, 2011. 145-157.[doi:10.1007/978-3-642-22993-0_16]
    [17] Lincoln P, Mitchell J, Scedrov A, Shankar N. Decision problems for propositional linear logic. Annals of Pure and Applied Logic, 1992,56(1-3):239-311.[doi:10.1016/0168-0072(92)90075-B]
    [18] Kanovich MI. Petri nets, Horn programs, linear logic, and vector games. Annals of Pure and Applied Logic, 1995,75(1-2):107-135.[doi:10.1016/0168-0072(94)00060-G]
    [19] Raskin JF, Samuelides M, Begin LV. Games for counting abstractions. Electronic Notes in Theoretical Computer Science, 2005,128(6):69-85.[doi:10.1016/j.entcs.2005.04.005]
    [20] Urquhart A. The complexity of decision procedures in relevance logic Ⅱ. The Journal of Symbolic Logic, 1999,64(4):1774-1802.[doi:10.2307/2586811]
    [21] Cantor G. Ueber unendliche, lineare Punktmannichfaltigkeiten. Mathematische Annalen, 1883,21(4):545-591.[doi:10.1007/BF01446819]
    [22] Minsky ML. Computation:Finite and Infinite Machines. Prentice-Hall, Inc., 1967.
    [23] Schmitz S, Schnoebelen P. The power of well-structured systems. In:D'Argenio PR, Melgratti H, eds. Proc. of the Int'l Conf. on Concurrency Theory. Berlin:Springer-Verlag, 2013. 5-24.[doi:10.1007/978-3-642-40184-8_2]
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

李春淼,蔡小娟,李国强.良结构下推系统的可覆盖性问题的下界.软件学报,2018,29(10):3009-3020

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2017-02-18
  • 最后修改日期:2017-05-09
  • 在线发布日期: 2018-03-14
文章二维码
友情链接:中国科学院软件研究所中国计算机学会中国科学院国家自然科学基金委员会CCF数字图书馆Int'l J of Softw Info计算机系统应用
您是第19795250位访问者
版权所有：中国科学院软件研究所 京ICP备05046678号-3
地址：北京市海淀区中关村南四街4号,邮政编码：100190
电话：010-62562563 传真：010-62562533 Email：jos@iscas.ac.cn
技术支持：北京勤云科技发展有限公司

京公网安备 11040202500063号