Volume 31 Issue 1
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LIU Jin, DUAN Zhenhua, TIAN Cong. Multi-Matching Nested Languages[J]. Chinese Journal of Electronics, 2022, 31(1): 137-145. doi: 10.1049/cje.2020.00.228
Citation: LIU Jin, DUAN Zhenhua, TIAN Cong. Multi-Matching Nested Languages[J]. Chinese Journal of Electronics, 2022, 31(1): 137-145. doi: 10.1049/cje.2020.00.228

Multi-Matching Nested Languages

doi: 10.1049/cje.2020.00.228
Funds:  This work was supported by the National Natural Science Foundation of China (61732013, 61751207), the National Key Research and Development Program of China (2018AAA0103202), and Shaanxi Key Science and Technology Innovation Team Project (2019TD-001)
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  • Author Bio:

    was born in 1991. She received the B.E. degree in computer science and technology from Xidian University, Xi’an, China. She is a Ph.D. candidate of Xidian University. Her research interests include formal methods and program verification. (Email: liujin_xd@163.com)

    (corresponding author) was born in 1948. He received the Ph.D. degree in computer science from the University of Newcastle upon Tyne, U.K., in 1996. He is now a Professor of Xidian University, Fellow of China Computer Federation. His research interests include model checking, network computing, the theory and technology of high-confidence software. (Email: zhhduan@mail.xidian.edu.cn)

    was born in 1981. She received the Ph.D. degree in electronic engineering from Xidian University. She is now a Professor in Xidian University, Distinguished Member of China Computer Federation. Her research interests include formal methods, temporal logic and model checking. (Email: ctian@mail.xidian.edu.cn)

  • Received Date: 2020-08-03
  • Accepted Date: 2020-09-16
  • Available Online: 2021-09-16
  • Publish Date: 2022-01-05
  • The data with both a linear ordering and a hierarchically nested one-to-one matching of items is ubiquitous, including parenthesis matching languages and hypertext markup language/extensive markup language (HTML/XML) documents. There exist some real-world problems which are beyond one-to-one matching. They have a multi-matching structure including one-to-n or n-to-one matching relation. Multiple threads can simultaneously read the same file, one block of memory can be referenced by multiple pointers in programs. We propose a new model of multi-matching nested relations consisting of a sequence of linearly ordered call, return and internal positions and augmented with one-to-one, one-to-n or n-to-one matching nested edges from calls to returns. Via linear encoding by introducing tagged letters, multi-matching nested words are obtained over a tagged alphabet. We put forward multi-matching nested traceable automata and the accepted languages are called multi-matching nested languages. Multi-matching nested grammars are presented which have the same expressive power as the proposed automata. An application is displayed to illustrate how the automata work.
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