# Stream Processing using Grammars and Regular Expressions

Ulrik Terp Rasmussen

January, 2017

PhD Thesis

### Abstract

In this dissertation we study regular expression based parsing and the use of grammatical specifications for the synthesis of fast, streaming string-processing programs.

In the first part we develop two linear-time algorithms for regular expression based parsing with Perl-style greedy disambiguation. The first algorithm operates in two passes in a semi-streaming fashion, using a constant amount of working memory and an auxiliary tape storage which is written in the first pass and consumed by the second. The second algorithm is a single-pass and optimally streaming algorithm which outputs as much of the parse tree as is semantically possible based on the input prefix read so far, and resorts to buffering as many symbols as is required to resolve the next choice. Optimality is obtained by performing a PSPACE-complete pre-analysis on the regular expression.

In the second part we present Kleenex, a language for expressing high-performance streaming string processing programs as regular grammars with embedded semantic actions, and its compilation to streaming string transducers with worst-case linear-time performance. Its underlying theory is based on transducer decomposition into oracle and action machines, and a finite-state specialization of the streaming parsing algorithm presented in the first part. In the second part we also develop a new linear-time streaming parsing algorithm for parsing expression grammars (PEG) which generalizes the regular grammars of Kleenex. The algorithm is based on a bottom-up tabulation algorithm reformulated using least fixed points and evaluated using an instance of the chaotic iteration scheme by Cousot and Cousot.

@phdthesis{rasmussen2017,
title = {Stream {Processing} using {Grammars} and {Regular} {Expressions}},
note = {PhD Thesis},
abstract = {In this dissertation we study regular expression based parsing and the use of grammatical specifications for the synthesis of fast, streaming string-processing programs.
In the first part we develop two linear-time algorithms for regular expression based parsing with Perl-style greedy disambiguation. The first algorithm operates in two passes in a semi-streaming fashion, using a constant amount of working memory and an auxiliary tape storage which is written in the first pass and consumed by the second. The second algorithm is a single-pass and optimally streaming algorithm which outputs as much of the parse tree as is semantically possible based on the input prefix read so far, and resorts to buffering as many symbols as is required to resolve the next choice. Optimality is obtained by performing a PSPACE-complete pre-analysis on the regular expression.
In the second part we present Kleenex, a language for expressing high-performance streaming string processing programs as regular grammars with embedded semantic actions, and its compilation to streaming string transducers with worst-case linear-time performance. Its underlying theory is based on transducer decomposition into oracle and action machines, and a finite-state specialization of the streaming parsing algorithm presented in the first part. In the second part we also develop a new linear-time streaming parsing algorithm for parsing expression grammars (PEG) which generalizes the regular grammars of Kleenex. The algorithm is based on a bottom-up tabulation algorithm reformulated using least fixed points and evaluated using an instance of the chaotic iteration scheme by Cousot and Cousot.},
school = {University of Copenhagen},
author = {Ulrik Terp Rasmussen},
month = {January},
year = {2017},
}