diff -r c0c1ebe09c7d -r 8ffa28fce271 ChengsongTanPhdThesis/Chapters/RelatedWork.tex --- a/ChengsongTanPhdThesis/Chapters/RelatedWork.tex Sat Nov 12 00:37:23 2022 +0000 +++ b/ChengsongTanPhdThesis/Chapters/RelatedWork.tex Sat Nov 12 21:34:40 2022 +0000 @@ -15,13 +15,40 @@ with theoretical work on them being fairly recent. -Campaneu gave +Campaneu et al. studied regexes with back-references +in the context of formal languages theory in +their 2003 work \cite{campeanu2003formal}. +They devised a pumping lemma for Perl-like regexes, +proving that the langugages denoted by them +is properly contained in context-sensitive +languages. +More interesting questions such as +whether the language denoted by Perl-like regexes +can express palindromes ($\{w \mid w = w^R\}$) +are discussed in \cite{campeanu2009patterns} +and \cite{CAMPEANU2009Intersect}. +Freydenberger \cite{Frey2013} investigated the +expressive power of back-references. He showed several +undecidability and decriptional complexity results +of back-references, concluding that they add +great power to certain programming tasks but are difficult to harness. +An interesting question would then be +whether we can add restrictions to them, +so that they become expressive enough, but not too powerful. +Freydenberger and Schmid \cite{FREYDENBERGER20191} +introduced the notion of deterministic +regular expressions with back-references to achieve +a better balance between expressiveness and tractability. -See \cite{AHO1990255} for a survey +Fernau and Schmid \cite{FERNAU2015287} and Schmid \cite{Schmid2012} +investigated the time complexity of different variants +of back-references. + +See \cite{BERGLUND2022} for a survey of these works and comparison between different -flavours (e.g. whether references can be circular, -can labels be repeated etc.) of back-references syntax. +flavours of back-references syntax (e.g. whether references can be circular, +can labels be repeated etc.). \subsection{Matchers and Lexers with Mechanised Proofs}