Document

Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

This paper introduces a new automata-theoretic class of string-to-string functions with polynomial growth. Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive definitions that close the class of regular functions under certain operations. Our motivation for studying this class comes from another characterization, which we merely mention here but prove elsewhere, based on a λ-calculus with a linear type system.
As their name suggests, these comparison-free polyregular functions form a subclass of polyregular functions; we prove that the inclusion is strict. We also show that they are incomparable with HDT0L transductions, closed under usual function composition - but not under a certain "map" combinator - and satisfy a comparison-free version of the pebble minimization theorem.
On the broader topic of polynomial growth transductions, we also consider the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that a function can be obtained by composing such transducers together if and only if it is polyregular, and that k-layered SSTs (or k-marble transducers) are closed under "map" and equivalent to a corresponding notion of (k+1)-layered HDT0L systems.

Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Pierre Pradic. Comparison-Free Polyregular Functions. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 139:1-139:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.ICALP.2021.139, author = {Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and No\^{u}s, Camille and Pradic, Pierre}, title = {{Comparison-Free Polyregular Functions}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {139:1--139:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.139}, URN = {urn:nbn:de:0030-drops-142087}, doi = {10.4230/LIPIcs.ICALP.2021.139}, annote = {Keywords: pebble transducers, HDT0L systems, polyregular functions} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

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.

Lê Thành Dũng Nguyễn and Pierre Pradic. Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 135:1-135:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.ICALP.2020.135, author = {Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, Pierre}, title = {{Implicit Automata in Typed \lambda-Calculi I: Aperiodicity in a Non-Commutative Logic}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {135:1--135:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.135}, URN = {urn:nbn:de:0030-drops-125426}, doi = {10.4230/LIPIcs.ICALP.2020.135}, annote = {Keywords: Church encodings, ordered linear types, star-free languages} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

We introduce a new approach to implicit complexity in linear logic, inspired by functional database query languages and using recent developments in effective denotational semantics of polymorphism. We give the first sub-polynomial upper bound in a type system with impredicative polymorphism; adding restrictions on quantifiers yields a characterization of logarithmic space, for which extensional completeness is established via descriptive complexity.

Lê Thành Dũng Nguyễn and Pierre Pradic. From Normal Functors to Logarithmic Space Queries (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 123:1-123:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.ICALP.2019.123, author = {Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, Pierre}, title = {{From Normal Functors to Logarithmic Space Queries}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {123:1--123:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.123}, URN = {urn:nbn:de:0030-drops-106994}, doi = {10.4230/LIPIcs.ICALP.2019.123}, annote = {Keywords: coherence spaces, elementary linear logic, semantic evaluation} }

Document

**Published in:** LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, a non-classical subsystem of MSO, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.

Pierre Pradic and Colin Riba. A Curry-Howard Approach to Church's Synthesis. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{pradic_et_al:LIPIcs.FSCD.2017.30, author = {Pradic, Pierre and Riba, Colin}, title = {{A Curry-Howard Approach to Church's Synthesis}}, booktitle = {2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)}, pages = {30:1--30:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-047-7}, ISSN = {1868-8969}, year = {2017}, volume = {84}, editor = {Miller, Dale}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.30}, URN = {urn:nbn:de:0030-drops-77198}, doi = {10.4230/LIPIcs.FSCD.2017.30}, annote = {Keywords: Intuitionistic Arithmetic, Realizability, Monadic Second-Order Logic on Infinite Words} }

Document

**Published in:** LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

We study the strength of axioms needed to prove various results related to automata on infinite words and Büchi's theorem on the decidability of the MSO theory of (N, less_or_equal). We prove that the following are equivalent over the weak second-order arithmetic theory RCA:
1. Büchi's complementation theorem for nondeterministic automata on infinite words,
2. the decidability of the depth-n fragment of the MSO theory of (N, less_or_equal), for each n greater than 5,
3. the induction scheme for Sigma^0_2 formulae of arithmetic.
Moreover, each of (1)-(3) is equivalent to the additive version of Ramsey's Theorem for pairs, often used in proofs of (1); each of (1)-(3) implies McNaughton's determinisation theorem for automata on infinite words; and each of (1)-(3) implies the "bounded-width" version of König's Lemma, often used in proofs of McNaughton's theorem.

Leszek Aleksander Kolodziejczyk, Henryk Michalewski, Pierre Pradic, and Michal Skrzypczak. The Logical Strength of Büchi's Decidability Theorem. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{kolodziejczyk_et_al:LIPIcs.CSL.2016.36, author = {Kolodziejczyk, Leszek Aleksander and Michalewski, Henryk and Pradic, Pierre and Skrzypczak, Michal}, title = {{The Logical Strength of B\"{u}chi's Decidability Theorem}}, booktitle = {25th EACSL Annual Conference on Computer Science Logic (CSL 2016)}, pages = {36:1--36:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-022-4}, ISSN = {1868-8969}, year = {2016}, volume = {62}, editor = {Talbot, Jean-Marc and Regnier, Laurent}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.36}, URN = {urn:nbn:de:0030-drops-65765}, doi = {10.4230/LIPIcs.CSL.2016.36}, annote = {Keywords: nondeterministic automata, monadic second-order logic, B\"{u}chi's theorem, additive Ramsey's theorem, reverse mathematics} }