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A classical theorem states that the set of languages given by a pushdownautomaton coincides with the set of languages given by a context-free grammar.In previous work, we proved the pendant of this theorem in a setting withinteraction: the set of processes given by a pushdown automaton coincides withthe set of processes given by a finite guarded recursive specification over aprocess algebra with actions, choice, sequencing and guarded recursion, if andonly if we add sequential value passing. In this paper, we look what happens ifwe consider parallel pushdown automata instead of pushdown automata, and aprocess algebra with parallelism instead of sequencing.

Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)