A Counterexample to Shyamasundar's Characterization of Pushdown Permuters

There is a well-known class of algorithms for permuting symbols using a single pushdown stack, and a finite number of random access memory cells. Reingold [3] has formally characterized this class of algorithms by a device called a pushdown permuter (p.d.p.), and has attempted to characterize the type of permutations that can be achieved by a pushdown permuter. Carlson [l] has presented a counterexample to Reingold’s characterization. Shyamasundar [4] has also presented a characterization of this class of permutations. In this note we present a counterexample to Shyamasundar’s characterization. We refer the reader to any of the papers [l]-[4] for a detailed description of a p.d.p., and the operations it can perform.