Parallel Hyperedge Replacement String Languages
Graham Campbell (School of Mathematics, Statistics, Physics,, Newcastle University, Newcastle upon Tyne, United Kingdom)

TL;DR
This paper introduces a new class of formal languages called parallel hyperedge replacement string languages, which encompasses multiple context-free and ET0L languages, aiming to classify the word problems of hyperbolic groups within this hierarchy.
Contribution
It defines a novel language class and establishes its relation to existing classes, providing a foundation for future classification of hyperbolic group word problems.
Findings
Contains all multiple context-free languages
Includes all ET0L languages
Provides groundwork for classifying hyperbolic group word problems
Abstract
There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is a long-standing open question as to where to place the word problems of hyperbolic groups in the formal language hierarchy. In this paper, we introduce a new language class called the parallel hyperedge replacement string languages, show that it contains all multiple context-free and ET0L languages, and lay down the foundations for future work that may be able to place the word problems of many hyperbolic groups in this class.
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Taxonomy
TopicsDNA and Biological Computing · semigroups and automata theory · Algorithms and Data Compression
