IEICE TRANSACTIONS on Information
On Lookaheads in Regular Expressions with Backreferences
Summary :
Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewblp and the latter as rewbln). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid[2] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewblp or rewbln. To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewblp. The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewblp.
- Publication
- IEICE TRANSACTIONS on Information Vol.E106-D No.5 pp.959-975
- Publication Date
- 2023/05/01
- Publicized
- 2023/02/06
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2022EDP7098
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
Authors
Nariyoshi CHIDA
NTT Security Japan,Waseda University
Tachio TERAUCHI
Waseda University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Nariyoshi CHIDA, Tachio TERAUCHI, "On Lookaheads in Regular Expressions with Backreferences" in IEICE TRANSACTIONS on Information,
vol. E106-D, no. 5, pp. 959-975, May 2023, doi: 10.1587/transinf.2022EDP7098.
Abstract: Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewblp and the latter as rewbln). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid[2] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewblp or rewbln. To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewblp. The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewblp.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2022EDP7098/_p
Copy
@ARTICLE{e106-d_5_959,
author={Nariyoshi CHIDA, Tachio TERAUCHI, },
journal={IEICE TRANSACTIONS on Information},
title={On Lookaheads in Regular Expressions with Backreferences},
year={2023},
volume={E106-D},
number={5},
pages={959-975},
abstract={Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewblp and the latter as rewbln). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid[2] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewblp or rewbln. To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewblp. The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewblp.},
keywords={},
doi={10.1587/transinf.2022EDP7098},
ISSN={1745-1361},
month={May},}
Copy
TY - JOUR
TI - On Lookaheads in Regular Expressions with Backreferences
T2 - IEICE TRANSACTIONS on Information
SP - 959
EP - 975
AU - Nariyoshi CHIDA
AU - Tachio TERAUCHI
PY - 2023
DO - 10.1587/transinf.2022EDP7098
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E106-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2023
AB - Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewblp and the latter as rewbln). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid[2] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewblp or rewbln. To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewblp. The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewblp.
ER -
English
