Parallel string acceptance using lattice graphs

This paper describes a method of string acceptance with respect to a given grammar G by repeatedly applying the rules of G in parallel. The process differs from previous work in parallel string recognition in that when a rule, say @a->@b, is applied, @b is not replaced by @a; rather, a 'string bypass', consisting of @a, is created that joins the left context of @b to its right context. Thus, the process creates a 'lattice graph' in which any directed path from the least element to the greatest element is a string derivable (in reverse) by a sequence of rewritings of @s. For context-free grammars, this process does not lead to a combinatorial explosion, and could thus be used to parse strings very rapidly if suitable parallel hardware were available.