Paper Info
Title
Limitations of Coverability Trees for Context-Free Parallel Communicating Grammar Systems and Why these Grammar Systems are not Linear Space.
Abstract
Coverability trees offer a finite characterization of all the derivations of a context-free. parallel grammar system (CF-PCGS). Their finite nature implies that they necessarily omit some information about these derivations. We demonstrate that the omitted information is most if not all of the time too much, and so coverability trees are not useful as an analysis tool except for their limited use already considered in the paper that introduces them (namely, determining the decidability of certain decision problems over PCGS). We establish this result by invalidating an existing proof that synchronized CF-PCGS are less expressive than context-sensitive grammars. Indeed, we discover that this proof relies on coverability trees for CF-PCGS, but that such coverability trees do not in fact contain enough information to support the proof.
Year
DOI
Venue
2016
10.1142/S0129626416500122
PARALLEL PROCESSING LETTERS
Keywords
Field
DocType
Theory of computation,formal languages,formal grammar,Turing completeness,parallel communicating grammar system,coverability trees
Decision problem,Programming language,Formal language,Turing completeness,Regular tree grammar,Computer science,Theoretical computer science,Decidability,Grammar,Formal grammar,Theory of computation
Journal
Volume
Issue
ISSN
26
3
0129-6264
Citations 
PageRank 
References 
0
0.34
5
Authors
2
Name
Order
Citations
PageRank
Stefan D. Bruda16212.18
Mary Sarah Ruth Wilkin200.68