Abstract
We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep acts on the input string, any other sweep processes the output of the previous one. The iufst accepts by halting in an accepting state at the end of a sweep.First, we study constant sweep boundediufsts. We prove their computational power coincides with the class of regular languages. We show their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. We prove the NL-completeness of typical decision problems.Next, we analyze non-constant sweep boundediufsts. We show they can accept non-regular languages provided an at least logarithmic amount of sweeps is allowed. We exhibit a proper non-regular language hierarchy depending on sweep complexity. The non-semidecidability of typical decision problems is also addressed.
Highlights
Finite-state transducers are finite automata with an output and they have been studied at least since 1950s
We focus on constant sweep bounded iufsts
We study their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations
Summary
Finite-state transducers are finite automata with an output and they have been studied at least since 1950s. Another point of view is taken in [2, 13], where subsequently applied identical transducers are studied Such iterated finite-state transducers are considered as language generating devices starting with some symbol in the initial state of the transducer, iteratively applying in multiple sweeps the transducer to the output produced so far, and eventually halting in an accepting state of the transducer after a last sweep. We start our investigations of such devices having a fixed number k ≥ 1 of sweeps Since in this case the language accepted by a k-iufst is always a regular language, it is of interest to compare such devices with deterministic finite automata (dfa) by investigating their descriptional complexity and the state cost of implementing language operations. We exhibit a nonregular language hierarchy with respect to sweep complexity
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