Modular Descriptions of Regular Functions

Gastin, Paul

doi:10.1007/978-3-030-21363-3_1

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…The composition operation can be used in place of the chained-sum operator of [3], and also in place of the unambiguous 2-chained iteration of [5], preserving expressiveness. In yet another recent paper, [12] proposes simple functions like copy, duplicate and reverse along with function composition to capture regular word transductions.…”

Section: As An Example Consider the Sdrtesmentioning

confidence: 99%

SD-Regular Transducer Expressions for Aperiodic Transformations

Dartois

Gastin

Krishna

2021

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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FO transductions, aperiodic deterministic two-way transducers, as well as aperiodic streaming string transducers are all equivalent models for first order definable functions. In this paper, we solve the problem of expressions capturing first order definable functions, thereby generalizing the seminal SF=AP (star-free expressions = aperiodic languages) result of Schützenberger. Our result also generalizes a lesser known characterization by Schützenberger of aperiodic languages by SD-regular expressions (SD=AP). We show that every first order definable function over finite words captured by an aperiodic deterministic two-way transducer can be described with an SDregular transducer expression (SDRTE). An SDRTE is a regular expression where Kleene stars are used in a restricted way: they can appear only on aperiodic languages which are prefix codes of bounded synchronization delay. SDRTEs are constructed from simple functions using the combinators unambiguous sum (deterministic choice), Hadamard product, and unambiguous versions of the Cauchy product and the k-chained Kleene-star, where the star is restricted as mentioned. In order to construct an SDRTE associated with an aperiodic deterministic two-way transducer, (i) we concretize Schützenberger's SD=AP result, by proving that aperiodic languages are captured by SD-regular expressions which are unambiguous and stabilising; (ii) by structural induction on the unambiguous, stabilising SD-regular expressions describing the domain of the transducer, we construct SDRTEs. Finally, we also look at various formalisms equivalent to SDRTEs which use the function composition, allowing to trade the k-chained star for a 1-star.

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Section: As An Example Consider the Sdrtesmentioning

confidence: 99%

SD-Regular Transducer Expressions for Aperiodic Transformations

Dartois

Gastin

Krishna

2021

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Self Cite

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“…The composition operation can be used in place of the chained-sum operator of [3], and also in place of the unambiguous 2-chained iteration of [11], preserving expressiveness. In yet another recent paper, [17] proposes simple functions like copy, duplicate and reverse along with function composition to capture regular word transductions.…”

Section: Related Workmentioning

confidence: 99%

SD-Regular Transducer Expressions for Aperiodic Transformations

Dartois¹,

Gastin²,

Krishna³

2021

Preprint

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FO transductions, aperiodic deterministic two-way transducers, as well as aperiodic streaming string transducers are all equivalent models for first order definable functions. In this paper, we solve the long standing open problem of expressions capturing first order definable functions, thereby generalizing the seminal SF=AP (star free expressions = aperiodic languages) result of Schützenberger. Our result also generalizes a lesser known characterization by Schützenberger of aperiodic languages by SD-regular expressions (SD=AP). We show that every first order definable function over finite words captured by an aperiodic deterministic two-way transducer can be described with an SD-regular transducer expression (SDRTE). An SDRTE is a regular expression where Kleene stars are used in a restricted way: they can appear only on aperiodic languages which are prefix codes of bounded synchronization delay. SDRTEs are constructed from simple functions using the combinators unambiguous sum (deterministic choice), Hadamard product, and unambiguous versions of the Cauchy product and the k-chained Kleene-star, where the star is restricted as mentioned. In order to construct an SDRTE associated with an aperiodic deterministic two-way transducer, (i) we concretize Schützenberger's SD=AP result, by proving that aperiodic languages are captured by SD-regular expressions which are unambiguous and stabilising; (ii) by structural induction on the unambiguous, stabilising SD-regular expressions describing the domain of the transducer, we construct SDRTEs. Finally, we also look at various formalisms equivalent to SDRTEs which use the function composition, allowing to trade the k-chained star for a 1-star.

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Modular Descriptions of Regular Functions

Cited by 2 publications

References 21 publications

SD-Regular Transducer Expressions for Aperiodic Transformations

SD-Regular Transducer Expressions for Aperiodic Transformations

SD-Regular Transducer Expressions for Aperiodic Transformations

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