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**Published in:** LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

We introduce weighted one-deterministic-counter automata (odca). These are weighted one-counter automata (oca) with the property of counter-determinacy, meaning that all paths labelled by a given word starting from the initial configuration have the same counter-effect. Weighted odcas are a strict extension of weighted visibly ocas, which are weighted ocas where the input alphabet determines the actions on the counter.
We present a novel problem called the co-VS (complement to a vector space) reachability problem for weighted odcas over fields, which seeks to determine if there exists a run from a given configuration of a weighted odca to another configuration whose weight vector lies outside a given vector space. We establish two significant properties of witnesses for co-VS reachability: they satisfy a pseudo-pumping lemma, and the lexicographically minimal witness has a special form. It follows that the co-VS reachability problem is in 𝖯.
These reachability problems help us to show that the equivalence problem of weighted odcas over fields is in 𝖯 by adapting the equivalence proof of deterministic real-time ocas [Stanislav Böhm and Stefan Göller, 2011] by Böhm et al. This is a step towards resolving the open question of the equivalence problem of weighted ocas. Finally, we demonstrate that the regularity problem, the problem of checking whether an input weighted odca over a field is equivalent to some weighted automaton, is in 𝖯. We also consider boolean odcas and show that the equivalence problem for (non-deterministic) boolean odcas is in PSPACE, whereas it is undecidable for (non-deterministic) boolean ocas.

Prince Mathew, Vincent Penelle, Prakash Saivasan, and A.V. Sreejith. Weighted One-Deterministic-Counter Automata. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mathew_et_al:LIPIcs.FSTTCS.2023.39, author = {Mathew, Prince and Penelle, Vincent and Saivasan, Prakash and Sreejith, A.V.}, title = {{Weighted One-Deterministic-Counter Automata}}, booktitle = {43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)}, pages = {39:1--39:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-304-1}, ISSN = {1868-8969}, year = {2023}, volume = {284}, editor = {Bouyer, Patricia and Srinivasan, Srikanth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.39}, URN = {urn:nbn:de:0030-drops-194129}, doi = {10.4230/LIPIcs.FSTTCS.2023.39}, annote = {Keywords: One-counter automata, Equivalence, Weighted automata, Reachability} }

Document

**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

We study two formalisms that allow to compare transducers over words under origin semantics: rational and regular resynchronizers, and show that the former are captured by the latter. We then consider some instances of the following synthesis problem: given transducers T_1,T_2, construct a rational (resp. regular) resynchronizer R, if it exists, such that T_1 is contained in R(T_2) under the origin semantics. We show that synthesis of rational resynchronizers is decidable for functional, and even finite-valued, one-way transducers, and undecidable for relational one-way transducers. In the two-way setting, synthesis of regular resynchronizers is shown to be decidable for unambiguous two-way transducers. For larger classes of two-way transducers, the decidability status is open.

Sougata Bose, Shankara Narayanan Krishna, Anca Muscholl, Vincent Penelle, and Gabriele Puppis. On Synthesis of Resynchronizers for Transducers. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bose_et_al:LIPIcs.MFCS.2019.69, author = {Bose, Sougata and Krishna, Shankara Narayanan and Muscholl, Anca and Penelle, Vincent and Puppis, Gabriele}, title = {{On Synthesis of Resynchronizers for Transducers}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {69:1--69:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.69}, URN = {urn:nbn:de:0030-drops-110133}, doi = {10.4230/LIPIcs.MFCS.2019.69}, annote = {Keywords: String transducers, resynchronizers, synthesis} }

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**Published in:** LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when restricting to functions from words to words. Here we prove that decidability can be equally recovered the origin semantics, that was introduced by Bojanczyk in 2014. We prove that the equivalence and containment problems for two-way word transducers in the origin semantics are PSPACE-complete. We also consider a variant of the containment problem where two-way transducers are compared under the origin semantics, but in a more relaxed way, by allowing distortions of the origins. The possible distortions are described by means of a resynchronization relation. We propose MSO-definable resynchronizers and show that they preserve the decidability of the containment problem under resynchronizations.
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Sougata Bose, Anca Muscholl, Vincent Penelle, and Gabriele Puppis. Origin-Equivalence of Two-Way Word Transducers Is in PSPACE. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bose_et_al:LIPIcs.FSTTCS.2018.22, author = {Bose, Sougata and Muscholl, Anca and Penelle, Vincent and Puppis, Gabriele}, title = {{Origin-Equivalence of Two-Way Word Transducers Is in PSPACE}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {22:1--22:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-093-4}, ISSN = {1868-8969}, year = {2018}, volume = {122}, editor = {Ganguly, Sumit and Pandya, Paritosh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.22}, URN = {urn:nbn:de:0030-drops-99213}, doi = {10.4230/LIPIcs.FSTTCS.2018.22}, annote = {Keywords: Transducers, origin semantics, equivalence} }

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**Published in:** LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach à la Karp and Miller can still be used to solve termination and boundedness. We provide a decidable characterisation of runs that can be iterated arbitrarily many times, which is the main ingredient of Karp and Miller's approach. However, the resulting Karp and Miller procedure only gives a semi-algorithm for HOPVASS. In fact, we show that coverability, termination and boundedness are all undecidable for HOPVASS, even in the restricted subcase of one counter and an order 2 stack. On the bright side, we prove that this semi-algorithm is in fact an algorithm for higher-order pushdown automata.

Vincent Penelle, Sylvain Salvati, and Grégoire Sutre. On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{penelle_et_al:LIPIcs.FSTTCS.2018.44, author = {Penelle, Vincent and Salvati, Sylvain and Sutre, Gr\'{e}goire}, title = {{On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {44:1--44:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-093-4}, ISSN = {1868-8969}, year = {2018}, volume = {122}, editor = {Ganguly, Sumit and Pandya, Paritosh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.44}, URN = {urn:nbn:de:0030-drops-99432}, doi = {10.4230/LIPIcs.FSTTCS.2018.44}, annote = {Keywords: Higher-order pushdown automata, Vector addition systems, Boundedness problem, Termination problem, Coverability problem} }

Document

**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers.

Mikolaj Bojanczyk, Laure Daviaud, Bruno Guillon, and Vincent Penelle. Which Classes of Origin Graphs Are Generated by Transducers. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 114:1-114:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2017.114, author = {Bojanczyk, Mikolaj and Daviaud, Laure and Guillon, Bruno and Penelle, Vincent}, title = {{Which Classes of Origin Graphs Are Generated by Transducers}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {114:1--114:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.114}, URN = {urn:nbn:de:0030-drops-73984}, doi = {10.4230/LIPIcs.ICALP.2017.114}, annote = {Keywords: Streaming String Transducers, Origin Semantics, String-to-String Transductions, MSO Definability} }

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