Reversal-bounded multi-pushdown machines

This paper presents several representations of the recursively enumerable (r.e.) sets. The first states that every r.e. set is the homomorphic image of the intersection of two linear context-free languages. Another states that every r.e. set is accepted by an on-line Turing acceptor with two pushdown stores such that in every computation, each pushdown store can make at most one reversal (that is, one change from "pushing" to "popping"). It is shown that this automatatheoretic representation cannot be strengthened by restricting the acceptors to be either deterministic multitape, nondeterministic one-tape, or nondeterministic multicounter acceptors. An investigation of the properties of reversal-bounded computations suggests that reversal bounds are not a "natural" measure of computational complexity for multitape Turing acceptors. The above results are used to obtain an independence theorem for full semi-AFLs and an undecidability result for effective families of languages.