The paper introduces a new notion of delay for comparing executions of streaming string transducers (SSTs). The key insights are:
The delay between two SST executions should not depend on the order in which periodic output blocks are produced, but only on the positions where the periodic structure changes.
The authors define a delay measure delayℓ that compares the number of output positions produced up to the end of each block of length at most ℓ.
They prove that this delay notion is regular - there exists a finite automaton that can check whether the delay between two SST executions is bounded by a given constant.
The authors also prove that their delay notion is complete - two SSTs are equivalent if and only if their executions have a bounded delay. This result extends to other transducer models like deterministic two-way transducers and MSO transducers.
The regularity and completeness of the delay notion enable decidability of several problems for SSTs, like equivalence up to a fixed delay bound, which are undecidable in the general case.
The paper provides a robust and machine-independent way to compare the executions of powerful string-to-string transducers, with important applications in transducer theory and verification.
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