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Documents authored by Traytel, Dmitriy

Document
DOI: 10.4230/LIPIcs.ICDT.2022.11
Practical Relational Calculus Query Evaluation

Authors: Martin Raszyk, David Basin, Srđan Krstić, and Dmitriy Traytel

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

Abstract
The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management systems. We devise a new translation of an arbitrary RC query into two safe-range queries, for which the finiteness of the query’s evaluation result is guaranteed. Assuming an infinite domain, the two queries have the following meaning: The first is closed and characterizes the original query’s relative safety, i.e., whether given a fixed database, the original query evaluates to a finite relation. The second safe-range query is equivalent to the original query, if the latter is relatively safe. We compose our translation with other, more standard ones to ultimately obtain two SQL queries. This allows us to use standard database management systems to evaluate arbitrary RC queries. We show that our translation improves the time complexity over existing approaches, which we also empirically confirm in both realistic and synthetic experiments.
Cite as

Martin Raszyk, David Basin, Srđan Krstić, and Dmitriy Traytel. Practical Relational Calculus Query Evaluation. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{raszyk_et_al:LIPIcs.ICDT.2022.11,
  author =	{Raszyk, Martin and Basin, David and Krsti\'{c}, Sr{\d}an and Traytel, Dmitriy},
  title =	{{Practical Relational Calculus Query Evaluation}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{11:1--11:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.11},
  URN =		{urn:nbn:de:0030-drops-158857},
  doi =		{10.4230/LIPIcs.ICDT.2022.11},
  annote =	{Keywords: Relational calculus, relative safety, safe-range, query translation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.10
Verified Progress Tracking for Timely Dataflow

Authors: Matthias Brun, Sára Decova, Andrea Lattuada, and Dmitriy Traytel

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Large-scale stream processing systems often follow the dataflow paradigm, which enforces a program structure that exposes a high degree of parallelism. The Timely Dataflow distributed system supports expressive cyclic dataflows for which it offers low-latency data- and pipeline-parallel stream processing. To achieve high expressiveness and performance, Timely Dataflow uses an intricate distributed protocol for tracking the computation’s progress. We modeled the progress tracking protocol as a combination of two independent transition systems in the Isabelle/HOL proof assistant. We specified and verified the safety of the two components and of the combined protocol. To this end, we identified abstract assumptions on dataflow programs that are sufficient for safety and were not previously formalized.
Cite as

Matthias Brun, Sára Decova, Andrea Lattuada, and Dmitriy Traytel. Verified Progress Tracking for Timely Dataflow. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{brun_et_al:LIPIcs.ITP.2021.10,
  author =	{Brun, Matthias and Decova, S\'{a}ra and Lattuada, Andrea and Traytel, Dmitriy},
  title =	{{Verified Progress Tracking for Timely Dataflow}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.10},
  URN =		{urn:nbn:de:0030-drops-139057},
  doi =		{10.4230/LIPIcs.ITP.2021.10},
  annote =	{Keywords: safety, distributed systems, timely dataflow, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.10
Generic Authenticated Data Structures, Formally

Authors: Matthias Brun and Dmitriy Traytel

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
Authenticated data structures are a technique for outsourcing data storage and maintenance to an untrusted server. The server is required to produce an efficiently checkable and cryptographically secure proof that it carried out precisely the requested computation. Recently, Miller et al. [https://doi.org/10.1145/2535838.2535851] demonstrated how to support a wide range of such data structures by integrating an authentication construct as a first class citizen in a functional programming language. In this paper, we put this work to the test of formalization in the Isabelle proof assistant. With Isabelle’s help, we uncover and repair several mistakes and modify the small-step semantics to perform call-by-value evaluation rather than requiring terms to be in administrative normal form.
Cite as

Matthias Brun and Dmitriy Traytel. Generic Authenticated Data Structures, Formally. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brun_et_al:LIPIcs.ITP.2019.10,
  author =	{Brun, Matthias and Traytel, Dmitriy},
  title =	{{Generic Authenticated Data Structures, Formally}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.10},
  URN =		{urn:nbn:de:0030-drops-110657},
  doi =		{10.4230/LIPIcs.ITP.2019.10},
  annote =	{Keywords: Authenticated Data Structures, Verifiable Computation, Isabelle/HOL, Nominal Isabelle}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.127
From Nondeterministic to Multi-Head Deterministic Finite-State Transducers (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Martin Raszyk, David Basin, and Dmitriy Traytel

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

Abstract
Every nondeterministic finite-state automaton is equivalent to a deterministic finite-state automaton. This result does not extend to finite-state transducers - finite-state automata equipped with a one-way output tape. There is a strict hierarchy of functions accepted by one-way deterministic finite-state transducers (1DFTs), one-way nondeterministic finite-state transducers (1NFTs), and two-way nondeterministic finite-state transducers (2NFTs), whereas the two-way deterministic finite-state transducers (2DFTs) accept the same family of functions as their nondeterministic counterparts (2NFTs). We define multi-head one-way deterministic finite-state transducers (mh-1DFTs) as a natural extension of 1DFTs. These transducers have multiple one-way reading heads that move asynchronously over the input word. Our main result is that mh-1DFTs can deterministically express any function defined by a one-way nondeterministic finite-state transducer. Of independent interest, we formulate the all-suffix regular matching problem, which is the problem of deciding for each suffix of an input word whether it belongs to a regular language. As part of our proof, we show that an mh-1DFT can solve all-suffix regular matching, which has applications, e.g., in runtime verification.
Cite as

Martin Raszyk, David Basin, and Dmitriy Traytel. From Nondeterministic to Multi-Head Deterministic Finite-State Transducers (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. 127:1-127:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{raszyk_et_al:LIPIcs.ICALP.2019.127,
  author =	{Raszyk, Martin and Basin, David and Traytel, Dmitriy},
  title =	{{From Nondeterministic to Multi-Head Deterministic Finite-State Transducers}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{127:1--127:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.127},
  URN =		{urn:nbn:de:0030-drops-107037},
  doi =		{10.4230/LIPIcs.ICALP.2019.127},
  annote =	{Keywords: Formal languages, Nondeterminism, Multi-head automata, Finite transducers}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.11
Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

Authors: Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel

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

Abstract
We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below epsilon-0. In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes. Our formal library also provides, somewhat nonstandardly, multisets with negative multiplicities and syntactic ordinals with negative coefficients. We present applications of the library to formalizations of Goodstein's theorem and the decidability of unary PCF (programming computable functions).
Cite as

Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel. Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{blanchette_et_al:LIPIcs.FSCD.2017.11,
  author =	{Blanchette, Jasmin Christian and Fleury, Mathias and Traytel, Dmitriy},
  title =	{{Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{11:1--11:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.11},
  URN =		{urn:nbn:de:0030-drops-77155},
  doi =		{10.4230/LIPIcs.FSCD.2017.11},
  annote =	{Keywords: Multisets, ordinals, proof assistants}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2016.31
Formal Languages, Formally and Coinductively

Authors: Dmitriy Traytel

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs of classic results in language theory. In this paper, we study this representation in the Isabelle proof assistant. We define regular operations on infinite tries and prove the axioms of Kleene algebra for those operations. Thereby, we exercise corecursion and coinduction and confirm the coinductive view being profitable in formalizations, as it improves over the set-of-words view with respect to proof automation.
Cite as

Dmitriy Traytel. Formal Languages, Formally and Coinductively. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{traytel:LIPIcs.FSCD.2016.31,
  author =	{Traytel, Dmitriy},
  title =	{{Formal Languages, Formally and Coinductively}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.31},
  URN =		{urn:nbn:de:0030-drops-59853},
  doi =		{10.4230/LIPIcs.FSCD.2016.31},
  annote =	{Keywords: Formal languages, codatatypes, corecursion, coinduction, interactive theorem proving, Isabelle HOL}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.487
A Coalgebraic Decision Procedure for WS1S

Authors: Dmitriy Traytel

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

Abstract
Weak monadic second-order logic of one successor (WS1S) is a simple and natural formalism to specify regular properties. WS1S is decidable, although the decision procedure's complexity is non-elementary. Typically, decision procedures for WS1S exploit the logic-automaton connection, i.e. they escape the simple and natural formalism by translating formulas into equally expressive regular structures such as finite automata, regular expressions, or games. In this work, we devise a coalgebraic decision procedure for WS1S that stays within the logical world by directly operating on formulas. The key operation is the derivative of a formula, modeled after Brzozowski's derivatives of regular expressions. The presented decision procedure has been formalized and proved correct in the interactive proof assistant Isabelle.
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Dmitriy Traytel. A Coalgebraic Decision Procedure for WS1S. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 487-503, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{traytel:LIPIcs.CSL.2015.487,
  author =	{Traytel, Dmitriy},
  title =	{{A Coalgebraic Decision Procedure for WS1S}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{487--503},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.487},
  URN =		{urn:nbn:de:0030-drops-54335},
  doi =		{10.4230/LIPIcs.CSL.2015.487},
  annote =	{Keywords: WS1S, decision procedure, coalgebra, Brzozowski derivatives, Isabelle}
}
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