Jumping Scattered Context Grammars

Conceptually, jumping scattered context grammars coincide with their standard counterparts, but they work differently. Indeed, a jumping version can apply a rule of the form (A1, A2, ..., An) -> (x1, x2, ..., xn) so it simultaneously erases A1, A2, ..., An in the current sentential form while inserting x1, x2, ..., xn possibly at different positions than the erased nonterminals. In fact, this paper introduces and studies scattered context grammars working under nine different jumping derivation modes, all of which give rise to the computational completeness. Indeed, the paper characterize the family of recursively enumerable languages by scattered context grammars working under any of these jumping modes. In its conclusion, the paper sketches application perspectives and formulates several open problems.