Document

**Published in:** LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

We study the class of rational recursive sequences (ratrec) over the rational numbers. A ratrec sequence is defined via a system of sequences using mutually recursive equations of depth 1, where the next values are computed as rational functions of the previous values. An alternative class is that of simple ratrec sequences, where one uses a single recursive equation, however of depth k: the next value is defined as a rational function of k previous values.
We conjecture that the classes ratrec and simple ratrec coincide. The main contribution of this paper is a proof of a variant of this conjecture where the initial conditions are treated symbolically, using a formal variable per sequence, while the sequences themselves consist of rational functions over those variables. While the initial conjecture does not follow from this variant, we hope that the introduced algebraic techniques may eventually be helpful in resolving the problem.
The class ratrec strictly generalises a well-known class of polynomial recursive sequences (polyrec). These are defined like ratrec, but using polynomial functions instead of rational ones. One can observe that if our conjecture is true and effective, then we can improve the complexities of the zeroness and the equivalence problems for polyrec sequences. Currently, the only known upper bound is Ackermanian, which follows from results on polynomial automata. We complement this observation by proving a PSPACE lower bound for both problems for polyrec. Our lower bound construction also implies that the Skolem problem is PSPACE-hard for the polyrec class.

Lorenzo Clemente, Maria Donten-Bury, Filip Mazowiecki, and Michał Pilipczuk. On Rational Recursive Sequences. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{clemente_et_al:LIPIcs.STACS.2023.24, author = {Clemente, Lorenzo and Donten-Bury, Maria and Mazowiecki, Filip and Pilipczuk, Micha{\l}}, title = {{On Rational Recursive Sequences}}, booktitle = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)}, pages = {24:1--24:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-266-2}, ISSN = {1868-8969}, year = {2023}, volume = {254}, editor = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.24}, URN = {urn:nbn:de:0030-drops-176763}, doi = {10.4230/LIPIcs.STACS.2023.24}, annote = {Keywords: recursive sequences, polynomial automata, zeroness problem, equivalence problem} }

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)

We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the separator is fixed, or not. In each case, we show that separability can be decided in EXPTIME, and that separating automata of exponential size suffice. We obtain our results by reducing to infinite duration games with ω-regular winning conditions and applying the finite-memory determinacy theorem of Büchi and Landweber.

Lorenzo Clemente and Michał Skrzypczak. Deterministic and Game Separability for Regular Languages of Infinite Trees. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 126:1-126:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2021.126, author = {Clemente, Lorenzo and Skrzypczak, Micha{\l}}, title = {{Deterministic and Game Separability for Regular Languages of Infinite Trees}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {126:1--126:15}, 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.2021.126}, URN = {urn:nbn:de:0030-drops-141952}, doi = {10.4230/LIPIcs.ICALP.2021.126}, annote = {Keywords: separation, infinite trees, regular languages, deterministic automata, game automata} }

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**Published in:** LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

We study the universality and inclusion problems for register automata over equality data (A, =). We show that the universality L(B) = (Σ × A)^* and inclusion problems L(A) ⊆ L(B) B can be solved with 2-EXPTIME complexity when both automata are without guessing and B is unambiguous, improving on the currently best-known 2-EXPSPACE upper bound by Mottet and Quaas. When the number of registers of both automata is fixed, we obtain a lower EXPTIME complexity, also improving the EXPSPACE upper bound from Mottet and Quaas for fixed number of registers. We reduce inclusion to universality, and then we reduce universality to the problem of counting the number of orbits of runs of the automaton. We show that the orbit-counting function satisfies a system of bidimensional linear recursive equations with polynomial coefficients (linrec), which generalises analogous recurrences for the Stirling numbers of the second kind, and then we show that universality reduces to the zeroness problem for linrec sequences. While such a counting approach is classical and has successfully been applied to unambiguous finite automata and grammars over finite alphabets, its application to register automata over infinite alphabets is novel.
We provide two algorithms to decide the zeroness problem for bidimensional linear recursive sequences arising from orbit-counting functions. Both algorithms rely on techniques from linear non-commutative algebra. The first algorithm performs variable elimination and has elementary complexity. The second algorithm is a refined version of the first one and it relies on the computation of the Hermite normal form of matrices over a skew polynomial field. The second algorithm yields an EXPTIME decision procedure for the zeroness problem of linrec sequences, which in turn yields the claimed bounds for the universality and inclusion problems of register automata.

Corentin Barloy and Lorenzo Clemente. Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{barloy_et_al:LIPIcs.STACS.2021.8, author = {Barloy, Corentin and Clemente, Lorenzo}, title = {{Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata}}, booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)}, pages = {8:1--8:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-180-1}, ISSN = {1868-8969}, year = {2021}, volume = {187}, editor = {Bl\"{a}ser, Markus and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.8}, URN = {urn:nbn:de:0030-drops-136533}, doi = {10.4230/LIPIcs.STACS.2021.8}, annote = {Keywords: unambiguous register automata, universality and inclusion problems, multi-dimensional linear recurrence sequences} }

Document

**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

The deterministic membership problem for timed automata asks whether the timed language recognised by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the deterministic timed automaton is fixed. We show that the problem in all the other cases is undecidable, i.e., when either 1) the input nondeterministic timed automaton has two clocks or more, or 2) it uses epsilon transitions, or 3) the number of clocks of the output deterministic automaton is not fixed.

Lorenzo Clemente, Sławomir Lasota, and Radosław Piórkowski. Determinisability of One-Clock Timed Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{clemente_et_al:LIPIcs.CONCUR.2020.42, author = {Clemente, Lorenzo and Lasota, S{\l}awomir and Pi\'{o}rkowski, Rados{\l}aw}, title = {{Determinisability of One-Clock Timed Automata}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {42:1--42:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.42}, URN = {urn:nbn:de:0030-drops-128542}, doi = {10.4230/LIPIcs.CONCUR.2020.42}, annote = {Keywords: Timed automata, determinisation, deterministic membership problem} }

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

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

Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees. They extend regular and context-free grammars, and are equivalent to simply typed λY-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes.

David Barozzini, Lorenzo Clemente, Thomas Colcombet, and Paweł Parys. Cost Automata, Safe Schemes, and Downward Closures. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 109:1-109:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barozzini_et_al:LIPIcs.ICALP.2020.109, author = {Barozzini, David and Clemente, Lorenzo and Colcombet, Thomas and Parys, Pawe{\l}}, title = {{Cost Automata, Safe Schemes, and Downward Closures}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {109:1--109:18}, 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.2020.109}, URN = {urn:nbn:de:0030-drops-125169}, doi = {10.4230/LIPIcs.ICALP.2020.109}, annote = {Keywords: Cost logics, cost automata, downward closures, higher-order recursion schemes, safe recursion schemes} }

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 study a generalisation of Büchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton with epsilon transitions and only Player I can elapse time. We show that for fixed number of clocks and maximal numerical constant available to Player II, it is decidable whether she has a winning timed controller using these resources. More interestingly, we also show that the problem remains decidable even when the maximal numerical constant is not specified in advance, which is an important technical novelty not present in previous literature on timed games. We complement these two decidability result by showing undecidability when the number of clocks available to Player II is not fixed.
As an application of timed games, and our main motivation to study them, we show that they can be used to solve the deterministic separability problem for nondeterministic timed automata with epsilon transitions. This is a novel decision problem about timed automata which has not been studied before. We show that separability is decidable when the number of clocks of the separating automaton is fixed and the maximal constant is not. The problem whether separability is decidable without bounding the number of clocks of the separator remains an interesting open problem.

Lorenzo Clemente, Sławomir Lasota, and Radosław Piórkowski. Timed Games and Deterministic Separability. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 121:1-121:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2020.121, author = {Clemente, Lorenzo and Lasota, S{\l}awomir and Pi\'{o}rkowski, Rados{\l}aw}, title = {{Timed Games and Deterministic Separability}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {121:1--121:16}, 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.2020.121}, URN = {urn:nbn:de:0030-drops-125282}, doi = {10.4230/LIPIcs.ICALP.2020.121}, annote = {Keywords: Timed automata, separability problems, timed games} }

Document

**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature.

Lorenzo Clemente, Piotr Hofman, and Patrick Totzke. Timed Basic Parallel Processes. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{clemente_et_al:LIPIcs.CONCUR.2019.15, author = {Clemente, Lorenzo and Hofman, Piotr and Totzke, Patrick}, title = {{Timed Basic Parallel Processes}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {15:1--15:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.15}, URN = {urn:nbn:de:0030-drops-109171}, doi = {10.4230/LIPIcs.CONCUR.2019.15}, annote = {Keywords: Timed Automata, Petri Nets} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an integer sort. This subsumes analogous expressibility results previously known for finite and pushdown timed automata with untimed stack. As key technical tools, we use quantifier elimination for a fragment of hybrid linear arithmetic and for cyclic order atoms, and a reduction to register pushdown automata over cyclic order atoms.

Lorenzo Clemente and Slawomir Lasota. Binary Reachability of Timed Pushdown Automata via Quantifier Elimination and Cyclic Order Atoms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 118:1-118:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2018.118, author = {Clemente, Lorenzo and Lasota, Slawomir}, title = {{Binary Reachability of Timed Pushdown Automata via Quantifier Elimination and Cyclic Order Atoms}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {118:1--118:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.118}, URN = {urn:nbn:de:0030-drops-91228}, doi = {10.4230/LIPIcs.ICALP.2018.118}, annote = {Keywords: timed automata, reachability relation, timed pushdown automata, linear arithmetic} }

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

We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model, we surprisingly show decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is disjoint from the other? We supplement this result by proving undecidability of the same problem already for languages of visibly one counter automata.

Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, and Charles Paperman. Regular Separability of Parikh Automata. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 117:1-117:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2017.117, author = {Clemente, Lorenzo and Czerwinski, Wojciech and Lasota, Slawomir and Paperman, Charles}, title = {{Regular Separability of Parikh Automata}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {117:1--117:13}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.117}, URN = {urn:nbn:de:0030-drops-74971}, doi = {10.4230/LIPIcs.ICALP.2017.117}, annote = {Keywords: Regular separability problem, Parikh automata, integer vector addition systems, visible one counter automata, decidability, undecidability} }

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**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Given two families of sets F and G, the F-separability problem for G asks whether for two given sets U, V in G there exists a set S in F, such that U is included in S and V is disjoint with S. We consider two families of sets F: modular sets S which are subsets of N^d, defined as unions of equivalence classes modulo some natural number n in N, and unary sets, which extend modular sets by requiring equality below a threshold n, and equivalence modulo n above n. Our main result is decidability of modular- and unary-separability for the class G of reachability sets of Vector Addition Systems, Petri Nets, Vector Addition Systems with States, and for sections thereof.

Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, and Charles Paperman. Separability of Reachability Sets of Vector Addition Systems. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{clemente_et_al:LIPIcs.STACS.2017.24, author = {Clemente, Lorenzo and Czerwinski, Wojciech and Lasota, Slawomir and Paperman, Charles}, title = {{Separability of Reachability Sets of Vector Addition Systems}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {24:1--24:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.24}, URN = {urn:nbn:de:0030-drops-70091}, doi = {10.4230/LIPIcs.STACS.2017.24}, annote = {Keywords: separability, Petri nets, modular sets, unary sets, decidability} }

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**Published in:** LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine machine, and ordered annotated multi-pushdown systems. In each case, our procedure yields tight complexity.

Lorenzo Clemente, Pawel Parys, Sylvain Salvati, and Igor Walukiewicz. Ordered Tree-Pushdown Systems. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 163-177, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{clemente_et_al:LIPIcs.FSTTCS.2015.163, author = {Clemente, Lorenzo and Parys, Pawel and Salvati, Sylvain and Walukiewicz, Igor}, title = {{Ordered Tree-Pushdown Systems}}, booktitle = {35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)}, pages = {163--177}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-97-2}, ISSN = {1868-8969}, year = {2015}, volume = {45}, editor = {Harsha, Prahladh and Ramalingam, G.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.163}, URN = {urn:nbn:de:0030-drops-56470}, doi = {10.4230/LIPIcs.FSTTCS.2015.163}, annote = {Keywords: reachability analysis, saturation technique, pushdown automata, ordered pushdown automata, higher-order pushdown automata, higher-order recursive sche} }

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**Published in:** LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.

Lorenzo Clemente and Slawomir Lasota. Reachability Analysis of First-order Definable Pushdown Systems. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 244-259, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{clemente_et_al:LIPIcs.CSL.2015.244, author = {Clemente, Lorenzo and Lasota, Slawomir}, title = {{Reachability Analysis of First-order Definable Pushdown Systems}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {244--259}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-90-3}, ISSN = {1868-8969}, year = {2015}, volume = {41}, editor = {Kreutzer, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.244}, URN = {urn:nbn:de:0030-drops-54185}, doi = {10.4230/LIPIcs.CSL.2015.244}, annote = {Keywords: automata theory, pushdown systems, sets with atoms, saturation technique} }

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