From Two-Way Transducers to Regular Function Expressions

Abstract

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SD-Regular Transducer Expressions for Aperiodic Transformations

“…The proof technique in [5] is completely different from [3], and, being algebraic, allows a uniform treatment of the result for transductions over finite and infinite words. Subsequently, an alternative proof for the result of [3] appeared in [4].…”

“…The counter part of regular expressions for aperiodic languages are star-free expressions, which are obtained by using the complementation operation instead of Kleene-star. The generalization of this result to transformations has been an open problem, as mentioned in [3], [4] and [5]. One of the main challenges in generalizing this result to transformations is the difficulty in finding an analogue for the complementation operation on sets in the setting of transformations.…”

“…The fundamental correspondence between machines and logic at the language level has been generalized to transformations by Engelfreit and Hoogeboom [1], where regular transformations are defined by two-way transducers (2DFTs) as well as by the MSO transductions of Courcelle [2]. A generalization of Kleene's theorem to transformations can be found in [3], [4] and [5].…”

Modular Descriptions of Regular Functions

“…The idea is to start from basic functions, e.g., (1 | 0) means "read 1 and output 0", and to apply simple combinators generalizing regular expressions [4,2,12,5]. For instance, using the Kleene iteration, (1 | 0) * describes a function which replaces a sequence of 1's with a sequence of 0's of same length.…”

“…Once again, we obtain an equivalent formalism for describing regular functions: the regular transducer expressions using +, ·, , * , r- * , 2+, r-2+ as combinators [4,2,12,5]:…”