Nondeterministic streaming string transducers

Abstract

We introduce nondeterministic streaming string transducers (NSSTs) - a new computational model that can implement MSO-definable relations between strings. An NSST makes a single left-to-right pass on the input string and uses a finite set of string variables to compute the output. In each step, it reads one input symbol, and updates its string variables in parallel with a copyless assignment. We show that NSST are closed under sequential composition and that their expressive power coincides with that of nondeterministic MSO-definable transductions. Further, we identify the class of functional NSSTs; such an NSST allows nondeterministic transitions, but for every successful run on a given input generates the same output string. We show that deciding functionality of an arbitrary NSST is decidable with PSPACE complexity, while the equivalence problem for functional NSSTs is PSPACE-complete. We also show that checking if the set of outputs of an NSST is contained within the set of outputs of a finite number of DSSTs is decidable in PSPACE. © 2011 Springer-Verlag.