Nondeterministic Streaming String Transducers

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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.