On Efficient Recognition of Transductions and Relations

Abstract We give some new or improved algorithms for recognizing transductions, relations and languages defined by pushdown machines, counter machines, etc. For example, we show that transductions defined by κ-tape one-way nondeterministic pushdown acceptors with outputs can be recognized in CFL( n κ ) time, where CFL( n ) is the multitape TM or unit-cost random access machine (RAM) complexity of context-free language recognition. When the pushdown store makes only one-turn or the pushdown store is replaced by a counter, we have RAM algorithms that run in O (n 2κ / log 2κ (2κ−1) n) and O (n κ+1 / log (κ+1) κ n) time respectively. Thus, linear context-free languages and one-counter languages are recognizable in O( n 2 /log 2 n ) time, which is an improvement over previously known algorithms. We also show that relations accepted by κ-tape two-way nondeterministic finite-state acceptors can be recognized in O( n κ ) time on a RAM, which improves another known result. Our methods use translation, dynamic programming with ‘precomputation’ and depth-first search.