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Implicit automata in typed λ-calculi I: aperiodicity in a non-commutative logic

Abstract : We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity in implicit computational complexity.
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https://hal.archives-ouvertes.fr/hal-02476219
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Submitted on : Wednesday, April 22, 2020 - 3:17:06 AM
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  • HAL Id : hal-02476219, version 2

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Lê Thành Dũng Nguyễn, Pierre Pradic. Implicit automata in typed λ-calculi I: aperiodicity in a non-commutative logic. 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Jul 2020, Saarbrücken (virtual conference), Germany. ⟨hal-02476219v2⟩

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