Not Seeing the Parse Trees from the Parse Forest of a Context-Free Parallel Communicating Grammar System

Parallel communicating grammar systems (PCGS) were introduced awhile ago purportedly to analyze concurrent systems on a language-theoretic level. To our knowledge however no actual relationship between PCGS and practical computing systems was ever investigated. We believe that PGCS with context-free components (CF-PCGS) have high practical potential, especially in the area of formal methods, so we started to bring CF-PCGS to a more practical level by studying a construct that has proven useful elsewhere: the parse tree (and forest). We show first that the original definition we introduced earlier falls short of all the desired properties: While each derivation has a corresponding parse forest, there are parse forests that do not correspond to any derivation, this applies to all the CF-PCGS variants. Because of this limitation we introduce a tighter version of parse trees (and forests) for CF-PCGS. Unfortunately we find that the new version does not bring any advantage over the original definition except for one, very restrictive variant of CF-PCGS. Overall beside providing a convenient tool to be used in conjunction with CF-PCGS, this work strongly suggests the aforementioned PCGS variant as the most promising model for practical applications in general and for grammatical approaches to formal verification of concurrent, recursive systems in particular.