From Compactifying Lambda-Letrec Terms to Recognizing Regular-Expression Processes

TL;DR

This paper explores the connection between lambda-calculus with letrec and regular-expression processes, proposing graph-based representations to facilitate translation and recognition between these computational models.

Contribution

It introduces a framework for structure-constrained graphs that bridge lambda-terms, term graphs, and process graphs, enabling better understanding and manipulation of these models.

Findings

Graph representations enable translation between lambda-terms and term graphs.

Recognition of regular-expression process graphs is facilitated by structure-constrained graphs.

The approach provides insights into the structure of finite-state processes and lambda-calculus terms.

Abstract

As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second, on Milner's process interpretation of regular expressions, a proper subclass of the finite-state processes. The aim of my talk was to motivate a transferal of ideas for workable concepts of structure-constrained graphs: from the problem of finding compact graph representations for terms in the lambda-calculus with letrec to the problem of recognizing finite process graphs that can be expressed by regular expressions. In both cases the construction of structure-constrained graphs was expedient in order to enable to go back and forth easily between, in the first case, lambda-terms and term graphs, and in the second case, regular expressions and process graphs. The main focus here is on providing pointers to my work with co-authors, in both areas separately. A secondary focus is on explaining directions of my present projects, and describing research questions of possibly general interest that have developed out of my work in these two areas.