A uniquely parsable unification grammar (UPUG) is a formal grammar with the following features: (1) parsing is performed without backtracking, and (2) each nonterminal symbol can have arguments, and derivation and parsing processes accompany unification of terms as in Prolog (or logic programming). We newly introduce a uniquely parallel parsable unification grammar (UPPUG) by extending the framework of a UPUG so that parallel parsing is also possible. We show that, in UPPUG, parsing can be done without backtracking in both cases of parallel and sequential reductions. We give examples of UPPUGs where a given input string can be parsed in sublinear number of steps of the length of the input by parallel reduction.

We propose a parallel parsing algorithm based on Earley's method, which works in O(log2n) time using O(n4.752) processors on CREW PRAM. This algorithm runs with less number of precessors compared with previously proposed W. Rytter's algorithm.