Work-sensitive Dynamic Complexity of Formal Languages

TL;DR

This paper investigates the parallel computational resources needed for dynamically updating query results for formal languages in constant time, introducing a framework for specifying such dynamic, parallel, constant-time programs with minimal work.

Contribution

It proposes a new framework based on dynamic descriptive complexity to analyze the work required for parallel, constant-time updates of language membership and range queries.

Findings

Framework for dynamic, parallel, constant-time programs

Analysis of work complexity for language queries

Insights into resource requirements for dynamic updates

Abstract

Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic, parallel, constant-time programs that require small amounts of work. This framework is based on the dynamic descriptive complexity framework by Patnaik and Immerman.