Single-Pass List Processing Algorithms as MSO-Definable Transducers

Two-way deterministic finite-state transducers define (partial) functions from input words to output words. This class of “regular” transductions has appealing theoretical properties, including a logical MSO-based characterization. We introduce a new kind of a transducer, heap-based (deterministic) transducer , that reads the input word from left to right in a single pass, and computes the output using a heap of cells storing output symbols and connected by next pointers. Using a finite number of pointer variables ranging over the heap cells, the transducer can dynamically update the heap structure by adding new cells and changing next-pointers. We prove that our model is expressively equivalent to the classical two-way model. We also establish Pspace bounds for the problems of checking equivalence of two heap-based transducers, and of checking whether a heap-based transducer satisfies pre/post verification conditions specified by automata over input/output words.