Theory Of Regular Expressions Research Articles

Synthesizing bijective lenses

Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as parsers and pretty printers, as database views and view updaters, and as a multitude of different kinds of ad hoc data converters. Manually building bidirectional transformations---by writing two separate functions that are intended to be inverses---is tedious and error prone. A better approach is to use a domain-specific language in which both directions can be written as a single expression. However, these domain-specific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. We present an alternative approach. Instead of coding transformations manually, we synthesize them from declarative format descriptions and examples. Specifically, we present Optician, a tool for type-directed synthesis of bijective string transformers. The inputs to Optician are a pair of ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a well-typed program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently. In particular, and unlike most prior work on type-directed synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). Consequently, program synthesis requires search in two dimensions: First, our synthesis algorithm must find a pair of "syntactically compatible types," and second, using the structure of those types, it must find a type- and example-compliant term. Our key insight is that it is possible to reduce the size of this search space without losing any computational power by defining a new language of lenses designed specifically for synthesis. The new language is free from arbitrary function composition and operates only over types and terms in a new disjunctive normal form. We prove (1) our new language is just as powerful as a more natural, compositional, and declarative language and (2) our synthesis algorithm is sound and complete with respect to the new language. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions, able to synthesize intricate lenses between complex file formats in seconds. We evaluate Optician on a benchmark suite of 39 examples that includes both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files.

Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)

The languages accepted by finite automata are precisely the l anguages denoted by regular expressions. In contrast, finite automata may exhibit behaviours t hat cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensi ons of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove that adding pure interleaving to the theory of regular expre ssions strictly increases its expressiveness modulo bisimilarity. Then, we prove that replacing the operation for pure interleaving by ACP-style parallel composition gives a further increase in expressiv eness. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata modulo bisimilarity. Our resu lts extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene’s star operation.

A Survey of Regular Expressions and Their Applications

This paper is an exposition of the theory of regular expressions and its applications to sequential circuits. The results of several authors are presented in a unified manner, pointing out the similarities and differences in the various treatments of the subject. Whenever possible, the terminology and notation of sequential circuit theory are used. The topics presented include: the relation of regular expressions to sequential circuits; algorithms for constructing sequential circuits and state diagrams corresponding to a given regular expression; methods for obtaining a regular expression from a state diagram of a sequential circuit, improper state diagrams, algebraic properties of regular expressions, and applications to codes.