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**Published in:** LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)

We study the problem of enumerating results from a query over a compressed document. The model we use for compression are straight-line programs (SLPs), which are defined by a context-free grammar that produces a single string. For our queries we use a model called Annotated Automata, an extension of regular automata that allows annotations on letters. This model extends the notion of Regular Spanners as it allows arbitrarily long outputs. Our main result is an algorithm which evaluates such a query by enumerating all results with output-linear delay after a preprocessing phase which takes linear time on the size of the SLP, and cubic time over the size of the automaton. This is an improvement over Schmid and Schweikardt’s result [Markus L. Schmid and Nicole Schweikardt, 2021], which, with the same preprocessing time, enumerates with a delay which is logarithmic on the size of the uncompressed document. We achieve this through a persistent data structure named Enumerable Compact Sets with Shifts which guarantees output-linear delay under certain restrictions. These results imply constant-delay enumeration algorithms in the context of regular spanners. Further, we use an extension of annotated automata which utilizes succinctly encoded annotations to save an exponential factor from previous results that dealt with constant-delay enumeration over vset automata. Lastly, we extend our results in the same fashion Schmid and Schweikardt did [Markus L. Schmid and Nicole Schweikardt, 2022] to allow complex document editing while maintaining the constant-delay guarantee.

Martín Muñoz and Cristian Riveros. Constant-Delay Enumeration for SLP-Compressed Documents. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{munoz_et_al:LIPIcs.ICDT.2023.7, author = {Mu\~{n}oz, Mart{\'\i}n and Riveros, Cristian}, title = {{Constant-Delay Enumeration for SLP-Compressed Documents}}, booktitle = {26th International Conference on Database Theory (ICDT 2023)}, pages = {7:1--7:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-270-9}, ISSN = {1868-8969}, year = {2023}, volume = {255}, editor = {Geerts, Floris and Vandevoort, Brecht}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.7}, URN = {urn:nbn:de:0030-drops-177495}, doi = {10.4230/LIPIcs.ICDT.2023.7}, annote = {Keywords: SLP compression, query evaluation, enumeration algorithms} }

Document

**Published in:** LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)

Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused on classes of centrality measures. In this work, we provide a different approach by focusing on classes of graphs instead of classes of measures to understand the underlying principles among various measures. More precisely, we study the class of trees. We observe that even in the case of trees, there is no consensus on which node should be selected as the most central. To analyze the behavior of centrality measures on trees, we introduce a property of tree rooting that states a measure selects one or two adjacent nodes as the most important, and the importance decreases from them in all directions. This property is satisfied by closeness centrality but violated by PageRank. We show that, for several centrality measures that root trees, the comparison of adjacent nodes can be inferred by potential functions that assess the quality of trees. We use these functions to give fundamental insights on rooting and derive a characterization explaining why some measure root trees. Moreover, we provide an almost linear time algorithm to compute the root of a graph by using potential functions. Finally, using a family of potential functions, we show that many ways of tree rooting exist with desirable properties.

Cristian Riveros, Jorge Salas, and Oskar Skibski. How Do Centrality Measures Choose the Root of Trees?. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{riveros_et_al:LIPIcs.ICDT.2023.12, author = {Riveros, Cristian and Salas, Jorge and Skibski, Oskar}, title = {{How Do Centrality Measures Choose the Root of Trees?}}, booktitle = {26th International Conference on Database Theory (ICDT 2023)}, pages = {12:1--12:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-270-9}, ISSN = {1868-8969}, year = {2023}, volume = {255}, editor = {Geerts, Floris and Vandevoort, Brecht}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.12}, URN = {urn:nbn:de:0030-drops-177545}, doi = {10.4230/LIPIcs.ICDT.2023.12}, annote = {Keywords: Databases, centrality measures, data centrality, graph theory, tree structures} }

Document

**Published in:** LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Some of the most relevant document schemas used online, such as XML and JSON, have a nested format. In the last decade, the task of extracting data from nested documents over streams has become especially relevant. We focus on the streaming evaluation of queries with outputs of varied sizes over nested documents. We model queries of this kind as Visibly Pushdown Transducers (VPT), a computational model that extends visibly pushdown automata with outputs and has the same expressive power as MSO over nested documents. Since processing a document through a VPT can generate a massive number of results, we are interested in reading the input in a streaming fashion and enumerating the outputs one after another as efficiently as possible, namely, with constant-delay. This paper presents an algorithm that enumerates these elements with constant-delay after processing the document stream in a single pass. Furthermore, we show that this algorithm is worst-case optimal in terms of update-time per symbol and memory usage.

Martín Muñoz and Cristian Riveros. Streaming Enumeration on Nested Documents. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 19:1-19:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{munoz_et_al:LIPIcs.ICDT.2022.19, author = {Mu\~{n}oz, Mart{\'\i}n and Riveros, Cristian}, title = {{Streaming Enumeration on Nested Documents}}, booktitle = {25th International Conference on Database Theory (ICDT 2022)}, pages = {19:1--19:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-223-5}, ISSN = {1868-8969}, year = {2022}, volume = {220}, editor = {Olteanu, Dan and Vortmeier, Nils}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.19}, URN = {urn:nbn:de:0030-drops-158935}, doi = {10.4230/LIPIcs.ICDT.2022.19}, annote = {Keywords: Streaming, nested documents, query evaluation, enumeration algorithms} }

Document

**Published in:** LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so through the lenses of parameterized dynamic data structures: we assume that the automaton is fixed and its size is the parameter, while the input word is revealed as in a stream, one symbol at a time following the natural order on positions. The goal is to design a dynamic data structure that can be efficiently updated upon revealing the next symbol, while maintaining the answer to the query on whether the word consisting of symbols revealed so far is accepted by the automaton. We provide complexity bounds for this dynamic acceptance problem for timed automata that process symbols interleaved with time spans. The main contribution is a dynamic data structure that maintains acceptance of a fixed one-clock timed automaton 𝒜 with amortized update time 2^{𝒪(|𝒜|)} per input symbol.

Alejandro Grez, Filip Mazowiecki, Michał Pilipczuk, Gabriele Puppis, and Cristian Riveros. Dynamic Data Structures for Timed Automata Acceptance. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grez_et_al:LIPIcs.IPEC.2021.20, author = {Grez, Alejandro and Mazowiecki, Filip and Pilipczuk, Micha{\l} and Puppis, Gabriele and Riveros, Cristian}, title = {{Dynamic Data Structures for Timed Automata Acceptance}}, booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)}, pages = {20:1--20:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-216-7}, ISSN = {1868-8969}, year = {2021}, volume = {214}, editor = {Golovach, Petr A. and Zehavi, Meirav}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.20}, URN = {urn:nbn:de:0030-drops-154037}, doi = {10.4230/LIPIcs.IPEC.2021.20}, annote = {Keywords: timed automata, data stream, dynamic data structure} }

Document

**Published in:** LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)

In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query one by one and without repetitions. This enumeration scheme is typically useful when the solutions are treated on the fly or when we want to stop the enumeration once the pertinent solutions have been found. However, with the current schemes, there is no restriction on the order how the solutions are given and this order usually depends on the techniques used and not on the relevance for the user.
In this paper we study the enumeration of monadic second order logic (MSO) over words when the solutions are ranked. We present a framework based on MSO cost functions that allows to express MSO formulae on words with a cost associated with each solution. We then demonstrate the generality of our framework which subsumes, for instance, document spanners and adds ranking to them. The main technical result of the paper is an algorithm for enumerating all the solutions of formulae in increasing order of cost efficiently, namely, with a linear preprocessing phase and logarithmic delay between solutions. The novelty of this algorithm is based on using functional data structures, in particular, by extending functional Brodal queues to suit with the ranked enumeration of MSO on words.

Pierre Bourhis, Alejandro Grez, Louis Jachiet, and Cristian Riveros. Ranked Enumeration of MSO Logic on Words. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 20:1-20:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bourhis_et_al:LIPIcs.ICDT.2021.20, author = {Bourhis, Pierre and Grez, Alejandro and Jachiet, Louis and Riveros, Cristian}, title = {{Ranked Enumeration of MSO Logic on Words}}, booktitle = {24th International Conference on Database Theory (ICDT 2021)}, pages = {20:1--20:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-179-5}, ISSN = {1868-8969}, year = {2021}, volume = {186}, editor = {Yi, Ke and Wei, Zhewei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.20}, URN = {urn:nbn:de:0030-drops-137286}, doi = {10.4230/LIPIcs.ICDT.2021.20}, annote = {Keywords: Persistent data structures, Query evaluation, Enumeration algorithms} }

Document

**Published in:** LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Complex event processing (CEP) has gained a lot of attention for evaluating complex patterns over high-throughput data streams. Recently, new algorithms for the evaluation of CEP patterns have emerged with strong guarantees of efficiency, i.e. constant update-time per tuple and constant-delay enumeration. Unfortunately, these techniques are restricted for patterns with local filters, limiting the possibility of using joins for correlating the data of events that are far apart.
In this paper, we embark on the search for efficient evaluation algorithms of CEP patterns with joins. We start by formalizing the so-called partition-by operator, a standard operator in data stream management systems to correlate contiguous events on streams. Although this operator is a restricted version of a join query, we show that partition-by (without iteration) is equally expressive as hierarchical queries, the biggest class of full conjunctive queries that can be evaluated with constant update-time and constant-delay enumeration over streams. To evaluate queries with partition-by we introduce an automata model, called chain complex event automata (chain-CEA), an extension of complex event automata that can compare data values by using equalities and disequalities. We show that this model admits determinization and is expressive enough to capture queries with partition-by. More importantly, we provide an algorithm with constant update time and constant delay enumeration for evaluating any query definable by chain-CEA, showing that all CEP queries with partition-by can be evaluated with these strong guarantees of efficiency.

Alejandro Grez and Cristian Riveros. Towards Streaming Evaluation of Queries with Correlation in Complex Event Processing. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 14:1-14:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{grez_et_al:LIPIcs.ICDT.2020.14, author = {Grez, Alejandro and Riveros, Cristian}, title = {{Towards Streaming Evaluation of Queries with Correlation in Complex Event Processing}}, booktitle = {23rd International Conference on Database Theory (ICDT 2020)}, pages = {14:1--14:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-139-9}, ISSN = {1868-8969}, year = {2020}, volume = {155}, editor = {Lutz, Carsten and Jung, Jean Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.14}, URN = {urn:nbn:de:0030-drops-119389}, doi = {10.4230/LIPIcs.ICDT.2020.14}, annote = {Keywords: Complex event processing, Query languages, Correlation, Constant delay enumeration.} }

Document

**Published in:** LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Complex Event Recognition (CER for short) has recently gained attention as a mechanism for detecting patterns in streams of continuously arriving event data. Numerous CER systems and languages have been proposed in the literature, commonly based on combining operations from regular expressions (sequencing, iteration, and disjunction) and relational algebra (e.g., joins and filters). While these languages are naturally first-order, meaning that variables can only bind single elements, they also provide capabilities for filtering sets of events that occur inside iterative patterns; for example requiring sequences of numbers to be increasing. Unfortunately, these type of filters usually present ad-hoc syntax and under-defined semantics, precisely because variables cannot bind sets of events. As a result, CER languages that provide filtering of sequences commonly lack rigorous semantics and their expressive power is not understood.
In this paper we embark on two tasks: First, to define a denotational semantics for CER that naturally allows to bind and filter sets of events; and second, to compare the expressive power of this semantics with that of CER languages that only allow for binding single events. Concretely, we introduce Set-Oriented Complex Event Logic (SO-CEL for short), a variation of the CER language introduced in [Grez et al., 2019] in which all variables bind to sets of matched events. We then compare SO-CEL with CEL, the CER language of [Grez et al., 2019] where variables bind single events. We show that they are equivalent in expressive power when restricted to unary predicates but, surprisingly, incomparable in general. Nevertheless, we show that if we restrict to sets of binary predicates, then SO-CEL is strictly more expressive than CEL. To get a better understanding of the expressive power, computational capabilities, and limitations of SO-CEL, we also investigate the relationship between SO-CEL and Complex Event Automata (CEA), a natural computational model for CER languages. We define a property on CEA called the *-property and show that, under unary predicates, SO-CEL captures precisely the subclass of CEA that satisfy this property. Finally, we identify the operations that SO-CEL is lacking to characterize CEA and introduce a natural extension of the language that captures the complete class of CEA under unary predicates.

Alejandro Grez, Cristian Riveros, Martín Ugarte, and Stijn Vansummeren. On the Expressiveness of Languages for Complex Event Recognition. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 15:1-15:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{grez_et_al:LIPIcs.ICDT.2020.15, author = {Grez, Alejandro and Riveros, Cristian and Ugarte, Mart{\'\i}n and Vansummeren, Stijn}, title = {{On the Expressiveness of Languages for Complex Event Recognition}}, booktitle = {23rd International Conference on Database Theory (ICDT 2020)}, pages = {15:1--15:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-139-9}, ISSN = {1868-8969}, year = {2020}, volume = {155}, editor = {Lutz, Carsten and Jung, Jean Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.15}, URN = {urn:nbn:de:0030-drops-119390}, doi = {10.4230/LIPIcs.ICDT.2020.15}, annote = {Keywords: Query languages, Complex Event Recognition, Logics, Automata theory} }

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**Published in:** LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of "relevant subgraphs" by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width.

Cristian Riveros and Jorge Salas. A Family of Centrality Measures for Graph Data Based on Subgraphs. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 23:1-23:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{riveros_et_al:LIPIcs.ICDT.2020.23, author = {Riveros, Cristian and Salas, Jorge}, title = {{A Family of Centrality Measures for Graph Data Based on Subgraphs}}, booktitle = {23rd International Conference on Database Theory (ICDT 2020)}, pages = {23:1--23:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-139-9}, ISSN = {1868-8969}, year = {2020}, volume = {155}, editor = {Lutz, Carsten and Jung, Jean Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.23}, URN = {urn:nbn:de:0030-drops-119474}, doi = {10.4230/LIPIcs.ICDT.2020.23}, annote = {Keywords: Graph data, graph centrality, centrality measures} }

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**Published in:** LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

Complex Event Processing (CEP) has emerged as the unifying field for technologies that require processing and correlating distributed data sources in real-time. CEP finds applications in diverse domains, which has resulted in a large number of proposals for expressing and processing complex events. However, existing CEP languages lack from a clear semantics, making them hard to understand and generalize. Moreover, there are no general techniques for evaluating CEP query languages with clear performance guarantees.
In this paper we embark on the task of giving a rigorous and efficient framework to CEP. We propose a formal language for specifying complex events, called CEL, that contains the main features used in the literature and has a denotational and compositional semantics. We also formalize the so-called selection strategies, which had only been presented as by-design extensions to existing frameworks. With a well-defined semantics at hand, we discuss how to efficiently process complex events by evaluating CEL formulas with unary filters. We start by studying the syntactical properties of CEL and propose rewriting optimization techniques for simplifying the evaluation of formulas. Then, we introduce a formal computational model for CEP, called complex event automata (CEA), and study how to compile CEL formulas with unary filters into CEA. Furthermore, we provide efficient algorithms for evaluating CEA over event streams using constant time per event followed by constant-delay enumeration of the results. Finally, we gather the main results of this work to present an efficient and declarative framework for CEP.

Alejandro Grez, Cristian Riveros, and Martín Ugarte. A Formal Framework for Complex Event Processing. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 5:1-5:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{grez_et_al:LIPIcs.ICDT.2019.5, author = {Grez, Alejandro and Riveros, Cristian and Ugarte, Mart{\'\i}n}, title = {{A Formal Framework for Complex Event Processing}}, booktitle = {22nd International Conference on Database Theory (ICDT 2019)}, pages = {5:1--5:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-101-6}, ISSN = {1868-8969}, year = {2019}, volume = {127}, editor = {Barcelo, Pablo and Calautti, Marco}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.5}, URN = {urn:nbn:de:0030-drops-103079}, doi = {10.4230/LIPIcs.ICDT.2019.5}, annote = {Keywords: Complex event processing, streaming evaluation, constant delay enumeration} }

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**Published in:** LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

We present three pumping lemmas for three classes of functions definable by fragments of weighted automata over the min-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus semiring.

Filip Mazowiecki and Cristian Riveros. Pumping Lemmas for Weighted Automata. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 50:1-50:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2018.50, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Pumping Lemmas for Weighted Automata}}, booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, pages = {50:1--50:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-062-0}, ISSN = {1868-8969}, year = {2018}, volume = {96}, editor = {Niedermeier, Rolf 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.2018.50}, URN = {urn:nbn:de:0030-drops-84984}, doi = {10.4230/LIPIcs.STACS.2018.50}, annote = {Keywords: Weighted automata, regular functions over words, pumping lemmas} }

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**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Probabilistic automata are a computational model introduced by Michael Rabin, extending nondeterministic finite automata with probabilistic transitions. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are undecidable. In this work we focus on the emptiness problem, which asks whether a given probabilistic automaton accepts some word with probability higher than a given threshold. We consider a natural and well-studied structural restriction on automata, namely the degree of ambiguity, which is defined as the maximum number of accepting runs over all words. We observe that undecidability of the emptiness problem requires infinite ambiguity and so we focus on the case of finitely ambiguous probabilistic automata.
Our main results are to construct efficient algorithms for analysing finitely ambiguous probabilistic automata through a reduction to a multi-objective optimisation problem, called the stochastic path problem. We obtain a polynomial time algorithm for approximating the value of finitely ambiguous probabilistic automata and a quasi-polynomial time algorithm for the emptiness problem for 2-ambiguous probabilistic automata.

Nathanaël Fijalkow, Cristian Riveros, and James Worrell. Probabilistic Automata of Bounded Ambiguity. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 19:1-19:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{fijalkow_et_al:LIPIcs.CONCUR.2017.19, author = {Fijalkow, Nathana\"{e}l and Riveros, Cristian and Worrell, James}, title = {{Probabilistic Automata of Bounded Ambiguity}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {19:1--19:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.19}, URN = {urn:nbn:de:0030-drops-77716}, doi = {10.4230/LIPIcs.CONCUR.2017.19}, annote = {Keywords: Probabilistic Automata, Emptiness Problem, Stochastic Path Problem, Multi-Objective Optimisation Problems} }

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**Published in:** LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study structural properties, expressiveness, and closure properties of copyless CRA. We show that copyless CRA are strictly less expressive than weighted automata and are not closed under reverse operation. To find a better class we impose restrictions on copyless CRA, which ends successfully with a new robust computational model that is closed under reverse and other extensions.

Filip Mazowiecki and Cristian Riveros. Copyless Cost-Register Automata: Structure, Expressiveness, and Closure Properties. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 53:1-53:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2016.53, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Copyless Cost-Register Automata: Structure, Expressiveness, and Closure Properties}}, booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)}, pages = {53:1--53:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-001-9}, ISSN = {1868-8969}, year = {2016}, volume = {47}, editor = {Ollinger, Nicolas and Vollmer, Heribert}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.53}, URN = {urn:nbn:de:0030-drops-57547}, doi = {10.4230/LIPIcs.STACS.2016.53}, annote = {Keywords: Cost Register Automata, Weighted Automata, Semirings} }

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

It is highly desirable for a computational model to have a logic characterization like in the seminal work from Buchi that connects MSO with finite automata. For example, weighted automata are the quantitative extension of finite automata for computing functions over words and they can be naturally characterized by a subframent of weighted logic introduced by Droste and Gastin. Recently, cost register automata (CRA) were introduced by Alur et al. as an alternative model for weighted automata. In hope of finding decidable subclasses of weighted automata, they proposed to restrict their model with the so-called copyless restriction. Unfortunately, copyless CRA do not enjoy good closure properties and, therefore, a logical characterization of this class seems to be unlikely.
In this paper, we introduce a new logic called maximal partition logic (MPL) for studying the expressiveness of copyless CRA. In contrast from the previous approaches (i.e. weighted logics), MPL is based on a new set of "regular" quantifiers that partition a word into maximal subwords, compute the output of a subformula over each subword separately, and then aggregate these outputs with a semiring operation. We study the expressiveness of MPL and compare it with weighted logics. Furthermore, we show that MPL is equally expressive to a natural subclass of copyless CRA. This shows the first logical characterization of copyless CRA and it gives a better understanding of the copyless restriction in weighted automata.

Filip Mazowiecki and Cristian Riveros. Maximal Partition Logic: Towards a Logical Characterization of Copyless Cost Register Automata. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 144-159, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{mazowiecki_et_al:LIPIcs.CSL.2015.144, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Maximal Partition Logic: Towards a Logical Characterization of Copyless Cost Register Automata}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {144--159}, 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.2015.144}, URN = {urn:nbn:de:0030-drops-54127}, doi = {10.4230/LIPIcs.CSL.2015.144}, annote = {Keywords: MSO, Finite Automata, Cost Register Automata, Weighted Automata, Weighted Logics, Semirings} }

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