8 Search Results for "Stanford, Caleb"

Document
DOI: 10.4230/LIPIcs.ITP.2025.16
Finiteness of Symbolic Derivatives in Lean

Authors: Ekaterina Zhuchko, Hendrik Maarand, Margus Veanes, and Gabriel Ebner

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Brzozowski proved that the set of derivatives of any regular expression is finite modulo associativity, idempotence and, notably, commutativity of the union operator. We extend this result to the case of symbolic location based derivatives, for which we prove finiteness of the state space by quotienting only by associativity, deduplication and idempotence (ADI); the fact that we don't use commutativity allows for this result to carry over to the derivative based backtracking (PCRE) match semantics, where the union operator is noncommutative. Furthermore, we consider regular expressions extended with lookarounds, intersection, and negation. We also show that our method for proving finiteness allows us to include certain simplification rules in the derivative operation while preserving finiteness. The finiteness proof is constructive: given an expression R, we construct a finite set that is an overapproximation (modulo ADI) of the set of derivatives of R. We reuse some of the infrastructure provided in previous formalization efforts for regular expressions in Lean 4, showing the flexibility and reusability of the framework.
Cite as

Ekaterina Zhuchko, Hendrik Maarand, Margus Veanes, and Gabriel Ebner. Finiteness of Symbolic Derivatives in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhuchko_et_al:LIPIcs.ITP.2025.16,
  author =	{Zhuchko, Ekaterina and Maarand, Hendrik and Veanes, Margus and Ebner, Gabriel},
  title =	{{Finiteness of Symbolic Derivatives in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.16},
  URN =		{urn:nbn:de:0030-drops-246144},
  doi =		{10.4230/LIPIcs.ITP.2025.16},
  annote =	{Keywords: Lean, regular languages, lookarounds, derivatives, finiteness}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.4
Bit-Precise Reasoning with Parametric Bit-Vectors

Authors: Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
The SMT-LIB theory of bit-vectors is restricted to bit-vectors of fixed width. However, several important applications can benefit from reasoning about bit-vectors of symbolic widths, i.e., parametric bit-vectors. Recent work has introduced an approach for solving formulas over parametric bit-vectors, via an eager translation to quantified integer arithmetic with uninterpreted functions. The approach was shown to be successful for several applications, including the bit-width independent verification of compiler optimizations, invertibility conditions, and rewrite rules. We extend and improve that approach in several aspects. Theoretically, we improve expressiveness by defining a new theory of parametric bit-vectors that supports more operators and allows reasoning about the bit-widths themselves. Algorithmically, we introduce a lazy algorithm that avoids the use of uninterpreted functions and quantified axioms for them. Empirically, we show a significant improvement by implementing and evaluating our approach, and comparing it experimentally to the previous one.
Cite as

Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli. Bit-Precise Reasoning with Parametric Bit-Vectors. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berger_et_al:LIPIcs.SAT.2025.4,
  author =	{Berger, Zvika and Zohar, Yoni and Niemetz, Aina and Preiner, Mathias and Reynolds, Andrew and Barrett, Clark and Tinelli, Cesare},
  title =	{{Bit-Precise Reasoning with Parametric Bit-Vectors}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.4},
  URN =		{urn:nbn:de:0030-drops-237385},
  doi =		{10.4230/LIPIcs.SAT.2025.4},
  annote =	{Keywords: Satisfiability Modulo Theories, Bit-precise Reasoning, Parametric Bit-vectors}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.31
Higher-Dimensional Automata: Extension to Infinite Tracks

Authors: Luc Passemard, Amazigh Amrane, and Uli Fahrenberg

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We introduce higher-dimensional automata for infinite interval ipomsets (ω-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by ω-HDAs under Büchi and Muller semantics. We show that Muller acceptance is more expressive than Büchi acceptance and, in contrast to the finite case, both semantics do not yield languages closed under subsumption. Then, we adapt the original rational operations to deal with ω-HDAs and show that while languages of ω-HDAs are ω-rational, not all ω-rational languages can be expressed by ω-HDAs.
Cite as

Luc Passemard, Amazigh Amrane, and Uli Fahrenberg. Higher-Dimensional Automata: Extension to Infinite Tracks. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{passemard_et_al:LIPIcs.FSCD.2025.31,
  author =	{Passemard, Luc and Amrane, Amazigh and Fahrenberg, Uli},
  title =	{{Higher-Dimensional Automata: Extension to Infinite Tracks}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.31},
  URN =		{urn:nbn:de:0030-drops-236466},
  doi =		{10.4230/LIPIcs.FSCD.2025.31},
  annote =	{Keywords: Higher-dimensional automata, concurrency theory, omega pomsets, B\"{u}chi acceptance, Muller acceptance, interval pomsets, pomsets with interfaces}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.16
A Strong Direct Sum Theorem for Distributional Query Complexity

Authors: Guy Blanc, Caleb Koch, Carmen Strassle, and Li-Yang Tan

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
Consider the expected query complexity of computing the k-fold direct product f^{⊗ k} of a function f to error ε with respect to a distribution μ^k. One strategy is to sequentially compute each of the k copies to error ε/k with respect to μ and apply the union bound. We prove a strong direct sum theorem showing that this naive strategy is essentially optimal. In particular, computing a direct product necessitates a blowup in both query complexity and error. Strong direct sum theorems contrast with results that only show a blowup in query complexity or error but not both. There has been a long line of such results for distributional query complexity, dating back to (Impagliazzo, Raz, Wigderson 1994) and (Nisan, Rudich, Saks 1994), but a strong direct sum theorem that holds for all functions in the standard query model had been elusive. A key idea in our work is the first use of the Hardcore Theorem (Impagliazzo 1995) in the context of query complexity. We prove a new resilience lemma that accompanies it, showing that the hardcore of f^{⊗k} is likely to remain dense under arbitrary partitions of the input space.
Cite as

Guy Blanc, Caleb Koch, Carmen Strassle, and Li-Yang Tan. A Strong Direct Sum Theorem for Distributional Query Complexity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 16:1-16:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blanc_et_al:LIPIcs.CCC.2024.16,
  author =	{Blanc, Guy and Koch, Caleb and Strassle, Carmen and Tan, Li-Yang},
  title =	{{A Strong Direct Sum Theorem for Distributional Query Complexity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{16:1--16:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.16},
  URN =		{urn:nbn:de:0030-drops-204123},
  doi =		{10.4230/LIPIcs.CCC.2024.16},
  annote =	{Keywords: Query complexity, direct product theorem, hardcore theorem}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2023.21
Automata Learning with an Incomplete Teacher

Authors: Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva

Published in: LIPIcs, Volume 263, 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Abstract
The preceding decade has seen significant interest in use of active learning to build models of programs and protocols. But existing algorithms assume the existence of an idealized oracle - a so-called Minimally Adequate Teacher (MAT) - that cannot be fully realized in practice and so is usually approximated with testing. This work proposes a new framework for active learning based on an incomplete teacher. This new formulation, called iMAT, neatly handles scenarios in which the teacher has access to only a finite number of tests or otherwise has gaps in its knowledge. We adapt Angluin’s L^⋆ algorithm for learning finite automata to incomplete teachers and we build a prototype implementation in OCaml that uses an SMT solver to help fill in information not supplied by the teacher. We demonstrate the behavior of our iMAT prototype on a variety of learning problems from a standard benchmark suite.
Cite as

Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva. Automata Learning with an Incomplete Teacher. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 21:1-21:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{moeller_et_al:LIPIcs.ECOOP.2023.21,
  author =	{Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra},
  title =	{{Automata Learning with an Incomplete Teacher}},
  booktitle =	{37th European Conference on Object-Oriented Programming (ECOOP 2023)},
  pages =	{21:1--21:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-281-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{263},
  editor =	{Ali, Karim and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2023.21},
  URN =		{urn:nbn:de:0030-drops-182145},
  doi =		{10.4230/LIPIcs.ECOOP.2023.21},
  annote =	{Keywords: Finite Automata, Active Learning, SMT Solvers}
}
Document
Artifact
DOI: 10.4230/DARTS.9.2.21
Automata Learning with an Incomplete Teacher (Artifact)

Authors: Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva

Published in: DARTS, Volume 9, Issue 2, Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Abstract
We provide an implementation of the automata learning software described in the associated ECOOP article. In particular, the artifact is a Docker image with the source code for nerode and nerode-learn, along with the scripts and benchmark inputs needed to reproduce the experiments described in the paper.
Cite as

Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva. Automata Learning with an Incomplete Teacher (Artifact). In Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 2, pp. 21:1-21:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{moeller_et_al:DARTS.9.2.21,
  author =	{Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra},
  title =	{{Automata Learning with an Incomplete Teacher (Artifact)}},
  pages =	{21:1--21:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2023},
  volume =	{9},
  number =	{2},
  editor =	{Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.9.2.21},
  URN =		{urn:nbn:de:0030-drops-182612},
  doi =		{10.4230/DARTS.9.2.21},
  annote =	{Keywords: Finite Automata, Active Learning, SMT Solvers}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.18
Certification with an NP Oracle

Authors: Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
In the certification problem, the algorithm is given a function f with certificate complexity k and an input x^⋆, and the goal is to find a certificate of size ≤ poly(k) for f’s value at x^⋆. This problem is in NP^NP, and assuming 𝖯 ≠ NP, is not in 𝖯. Prior works, dating back to Valiant in 1984, have therefore sought to design efficient algorithms by imposing assumptions on f such as monotonicity. Our first result is a BPP^NP algorithm for the general problem. The key ingredient is a new notion of the balanced influence of variables, a natural variant of influence that corrects for the bias of the function. Balanced influences can be accurately estimated via uniform generation, and classic BPP^NP algorithms are known for the latter task. We then consider certification with stricter instance-wise guarantees: for each x^⋆, find a certificate whose size scales with that of the smallest certificate for x^⋆. In sharp contrast with our first result, we show that this problem is NP^NP-hard even to approximate. We obtain an optimal inapproximability ratio, adding to a small handful of problems in the higher levels of the polynomial hierarchy for which optimal inapproximability is known. Our proof involves the novel use of bit-fixing dispersers for gap amplification.
Cite as

Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan. Certification with an NP Oracle. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blanc_et_al:LIPIcs.ITCS.2023.18,
  author =	{Blanc, Guy and Koch, Caleb and Lange, Jane and Strassle, Carmen and Tan, Li-Yang},
  title =	{{Certification with an NP Oracle}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.18},
  URN =		{urn:nbn:de:0030-drops-175217},
  doi =		{10.4230/LIPIcs.ITCS.2023.18},
  annote =	{Keywords: Certificate complexity, Boolean functions, polynomial hierarchy, hardness of approximation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.112
Automata-Based Stream Processing

Authors: Rajeev Alur, Konstantinos Mamouras, and Caleb Stanford

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

Abstract
We propose an automata-theoretic framework for modularly expressing computations on streams of data. With weighted automata as a starting point, we identify three key features that are useful for an automaton model for stream processing: expressing the regular decomposition of streams whose data items are elements of a complex type (e.g., tuple of values), allowing the hierarchical nesting of several different kinds of aggregations, and specifying modularly the parallel execution and combination of various subcomputations. The combination of these features leads to subtle efficiency considerations that concern the interaction between nondeterminism, hierarchical nesting, and parallelism. We identify a syntactic restriction where the nondeterminism is unambiguous and parallel subcomputations synchronize their outputs. For automata satisfying these restrictions, we show that there is a space- and time-efficient streaming evaluation algorithm. We also prove that when these restrictions are relaxed, the evaluation problem becomes inherently computationally expensive.
Cite as

Rajeev Alur, Konstantinos Mamouras, and Caleb Stanford. Automata-Based Stream Processing. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{alur_et_al:LIPIcs.ICALP.2017.112,
  author =	{Alur, Rajeev and Mamouras, Konstantinos and Stanford, Caleb},
  title =	{{Automata-Based Stream Processing}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{112:1--112:15},
  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.2017.112},
  URN =		{urn:nbn:de:0030-drops-74720},
  doi =		{10.4230/LIPIcs.ICALP.2017.112},
  annote =	{Keywords: weighted automata, Quantitative Regular Expressions, stream processing}
}
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