15 Search Results for "Traytel, Dmitriy"


Document
Seventeen Provers Under the Hammer

Authors: Martin Desharnais, Petar Vukmirović, Jasmin Blanchette, and Makarius Wenzel

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)


Abstract
One of the main success stories of automatic theorem provers has been their integration into proof assistants. Such integrations, or "hammers," increase proof automation and hence user productivity. In this paper, we use Isabelle/HOL’s Sledgehammer tool to find out how useful modern provers are at proving formulas in higher-order logic. Our evaluation follows in the steps of Böhme and Nipkow’s Judgment Day study from 2010, but instead of three provers we use 17, including SMT solvers and higher-order provers. Our work offers an alternative yardstick for comparing modern provers, next to the benchmarks and competitions emerging from the TPTP World and SMT-LIB.

Cite as

Martin Desharnais, Petar Vukmirović, Jasmin Blanchette, and Makarius Wenzel. Seventeen Provers Under the Hammer. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 8:1-8:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{desharnais_et_al:LIPIcs.ITP.2022.8,
  author =	{Desharnais, Martin and Vukmirovi\'{c}, Petar and Blanchette, Jasmin and Wenzel, Makarius},
  title =	{{Seventeen Provers Under the Hammer}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.8},
  URN =		{urn:nbn:de:0030-drops-167178},
  doi =		{10.4230/LIPIcs.ITP.2022.8},
  annote =	{Keywords: Automatic theorem proving, interactive theorem proving, proof assistants}
}
Document
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.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
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.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
Efficient Full Higher-Order Unification

Authors: Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)


Abstract
We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our unification procedure is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski’s procedure.

Cite as

Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin. Efficient Full Higher-Order Unification. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 5:1-5:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{vukmirovic_et_al:LIPIcs.FSCD.2020.5,
  author =	{Vukmirovi\'{c}, Petar and Bentkamp, Alexander and Nummelin, Visa},
  title =	{{Efficient Full Higher-Order Unification}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.5},
  URN =		{urn:nbn:de:0030-drops-123271},
  doi =		{10.4230/LIPIcs.FSCD.2020.5},
  annote =	{Keywords: unification, higher-order logic, theorem proving, term rewriting, indexing data structures}
}
Document
Coinduction in Flow: The Later Modality in Fibrations

Authors: Henning Basold

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
This paper provides a construction on fibrations that gives access to the so-called later modality, which allows for a controlled form of recursion in coinductive proofs and programs. The construction is essentially a generalisation of the topos of trees from the codomain fibration over sets to arbitrary fibrations. As a result, we obtain a framework that allows the addition of a recursion principle for coinduction to rather arbitrary logics and programming languages. The main interest of using recursion is that it allows one to write proofs and programs in a goal-oriented fashion. This enables easily understandable coinductive proofs and programs, and fosters automatic proof search. Part of the framework are also various results that enable a wide range of applications: transportation of (co)limits, exponentials, fibred adjunctions and first-order connectives from the initial fibration to the one constructed through the framework. This means that the framework extends any first-order logic with the later modality. Moreover, we obtain soundness and completeness results, and can use up-to techniques as proof rules. Since the construction works for a wide variety of fibrations, we will be able to use the recursion offered by the later modality in various context. For instance, we will show how recursive proofs can be obtained for arbitrary (syntactic) first-order logics, for coinductive set-predicates, and for the probabilistic modal mu-calculus. Finally, we use the same construction to obtain a novel language for probabilistic productive coinductive programming. These examples demonstrate the flexibility of the framework and its accompanying results.

Cite as

Henning Basold. Coinduction in Flow: The Later Modality in Fibrations. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{basold:LIPIcs.CALCO.2019.8,
  author =	{Basold, Henning},
  title =	{{Coinduction in Flow: The Later Modality in Fibrations}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{8:1--8:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.8},
  URN =		{urn:nbn:de:0030-drops-114369},
  doi =		{10.4230/LIPIcs.CALCO.2019.8},
  annote =	{Keywords: Coinduction, Fibrations, Later Modality, Recursive Proofs, Up-to techniques, Probabilistic Logic, Probabilistic Programming}
}
Document
Invited Paper
Coinduction: Automata, Formal Proof, Companions (Invited Paper)

Authors: Damien Pous

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
Coinduction is a mathematical tool that is used pervasively in computer science: to program and reason about infinite data-structures, to give semantics to concurrent systems, to obtain automata algorithms. We present some of these applications in automata theory and in formalised mathematics. Then we discuss recent developments on the abstract theory of coinduction and its enhancements.

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Damien Pous. Coinduction: Automata, Formal Proof, Companions (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{pous:LIPIcs.CALCO.2019.4,
  author =	{Pous, Damien},
  title =	{{Coinduction: Automata, Formal Proof, Companions}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{4:1--4:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.4},
  URN =		{urn:nbn:de:0030-drops-114323},
  doi =		{10.4230/LIPIcs.CALCO.2019.4},
  annote =	{Keywords: Coinduction, Automata, Coalgebra, Formal proofs}
}
Document
A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

Authors: Julian Brunner, Benedikt Seidl, and Salomon Sickert

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


Abstract
We present a formalisation of the unified translation approach from linear temporal logic (LTL) to omega-automata from [Javier Esparza et al., 2018]. This approach decomposes LTL formulas into "simple" languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction for deterministic Rabin automata (DRA). We extract from this particular instantiation an executable tool translating LTL to DRAs. To the best of our knowledge this is the first verified translation of LTL to DRAs that is proven to be double-exponential in the worst case which asymptotically matches the known lower bound.

Cite as

Julian Brunner, Benedikt Seidl, and Salomon Sickert. A Verified and Compositional Translation of LTL to Deterministic Rabin Automata. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{brunner_et_al:LIPIcs.ITP.2019.11,
  author =	{Brunner, Julian and Seidl, Benedikt and Sickert, Salomon},
  title =	{{A Verified and Compositional Translation of LTL to Deterministic Rabin Automata}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{11:1--11:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.11},
  URN =		{urn:nbn:de:0030-drops-110664},
  doi =		{10.4230/LIPIcs.ITP.2019.11},
  annote =	{Keywords: Automata Theory, Automata over Infinite Words, Deterministic Automata, Linear Temporal Logic, Model Checking, Verified Algorithms}
}
Document
Data Types as Quotients of Polynomial Functors

Authors: Jeremy Avigad, Mario Carneiro, and Simon Hudon

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


Abstract
A broad class of data types, including arbitrary nestings of inductive types, coinductive types, and quotients, can be represented as quotients of polynomial functors. This provides perspicuous ways of constructing them and reasoning about them in an interactive theorem prover.

Cite as

Jeremy Avigad, Mario Carneiro, and Simon Hudon. Data Types as Quotients of Polynomial Functors. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{avigad_et_al:LIPIcs.ITP.2019.6,
  author =	{Avigad, Jeremy and Carneiro, Mario and Hudon, Simon},
  title =	{{Data Types as Quotients of Polynomial Functors}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{6:1--6:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.6},
  URN =		{urn:nbn:de:0030-drops-110612},
  doi =		{10.4230/LIPIcs.ITP.2019.6},
  annote =	{Keywords: data types, polynomial functors, inductive types, coinductive types}
}
Document
Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq

Authors: Enrico Tassi

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


Abstract
We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations in Coq. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. First, we design appropriate induction principles for data types defined using parametric containers. Second, we develop a technique to work around the modularity limitations imposed by the purely syntactic termination check Coq performs on recursive proofs. The unary parametricity translation of inductive data types turns out to be the key to both steps. Last but not least, we provide an implementation of the procedure for the Coq proof assistant based on the Elpi [Dunchev et al., 2015] extension language.

Cite as

Enrico Tassi. Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{tassi:LIPIcs.ITP.2019.29,
  author =	{Tassi, Enrico},
  title =	{{Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{29:1--29:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.29},
  URN =		{urn:nbn:de:0030-drops-110841},
  doi =		{10.4230/LIPIcs.ITP.2019.29},
  annote =	{Keywords: Coq, Containers, Induction, Equality test, Parametricity translation}
}
Document
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.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
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.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
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.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
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.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
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.

Cite as

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.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}
}
Document
Modal Logics for Nominal Transition Systems

Authors: Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramunas Gutkovas, and Tjark Weber

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)


Abstract
We define a uniform semantic substrate for a wide variety of process calculi where states and action labels can be from arbitrary nominal sets. A Hennessy-Milner logic for these systems is introduced, and proved adequate for bisimulation equivalence. A main novelty is the use of finitely supported infinite conjunctions. We show how to treat different bisimulation variants such as early, late and open in a systematic way, and make substantial comparisons with related work. The main definitions and theorems have been formalized in Nominal Isabelle.

Cite as

Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramunas Gutkovas, and Tjark Weber. Modal Logics for Nominal Transition Systems. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 198-211, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{parrow_et_al:LIPIcs.CONCUR.2015.198,
  author =	{Parrow, Joachim and Borgstr\"{o}m, Johannes and Eriksson, Lars-Henrik and Gutkovas, Ramunas and Weber, Tjark},
  title =	{{Modal Logics for Nominal Transition Systems}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{198--211},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.198},
  URN =		{urn:nbn:de:0030-drops-53823},
  doi =		{10.4230/LIPIcs.CONCUR.2015.198},
  annote =	{Keywords: Process algebra, nominal sets, bisimulation, modal logic}
}
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