5 Search Results for "Horn, Paul"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.43
New Results on Cutting Plane Proofs for Horn Constraint Systems

Authors: Hans Kleine Büning, Piotr Wojciechowski, and K. Subramani

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
In this paper, we investigate properties of cutting plane based refutations for a class of integer programs called Horn constraint systems (HCS). Briefly, a system of linear inequalities A * x >= b is called a Horn constraint system, if each entry in A belongs to the set {0,1,-1} and furthermore there is at most one positive entry per row. Our focus is on deriving refutations i.e., proofs of unsatisfiability of such programs using cutting planes as a proof system. We also look at several properties of these refutations. Horn constraint systems can be considered as a more general form of propositional Horn formulas, i.e., CNF formulas with at most one positive literal per clause. Cutting plane calculus (CP) is a well-known calculus for deciding the unsatisfiability of propositional CNF formulas and integer programs. Usually, CP consists of a pair of inference rules. These are called the addition rule (ADD) and the division rule (DIV). In this paper, we show that cutting plane calculus is still complete for Horn constraints when every intermediate constraint is required to be Horn. We also investigate the lengths of cutting plane proofs for Horn constraint systems.
Cite as

Hans Kleine Büning, Piotr Wojciechowski, and K. Subramani. New Results on Cutting Plane Proofs for Horn Constraint Systems. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kleinebuning_et_al:LIPIcs.FSTTCS.2019.43,
  author =	{Kleine B\"{u}ning, Hans and Wojciechowski, Piotr and Subramani, K.},
  title =	{{New Results on Cutting Plane Proofs for Horn Constraint Systems}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.43},
  URN =		{urn:nbn:de:0030-drops-116056},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.43},
  annote =	{Keywords: Horn constraints, cutting planes, proof length}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.9
Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule

Authors: David Auger, Pierre Coucheney, and Yann Strozecki

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
The best algorithm so far for solving Simple Stochastic Games is Ludwig’s randomized algorithm [Ludwig, 1995] which works in expected 2^{O(sqrt{n})} time. We first give a simpler iterative variant of this algorithm, using Bland’s rule from the simplex algorithm, which uses exponentially less random bits than Ludwig’s version. Then, we show how to adapt this method to the algorithm of Gimbert and Horn [Gimbert and Horn, 2008] whose worst case complexity is O(k!), where k is the number of random nodes. Our algorithm has an expected running time of 2^{O(k)}, and works for general random nodes with arbitrary outdegree and probability distribution on outgoing arcs.
Cite as

David Auger, Pierre Coucheney, and Yann Strozecki. Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{auger_et_al:LIPIcs.STACS.2019.9,
  author =	{Auger, David and Coucheney, Pierre and Strozecki, Yann},
  title =	{{Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.9},
  URN =		{urn:nbn:de:0030-drops-102488},
  doi =		{10.4230/LIPIcs.STACS.2019.9},
  annote =	{Keywords: simple stochastic games, randomized algorithm, parametrized complexity, strategy improvement, Bland’s rule}
}
Document
DOI: 10.4230/OASIcs.ICLP.2018.18
Proof-Relevant Resolution for Elaboration of Programming Languages

Authors: Frantisek Farka

Published in: OASIcs, Volume 64, Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)

Abstract
Proof-relevant resolution is a new variant of resolution in Horn-clause logic and its extensions. We propose proof-relevant resolution as a systematic approach to elaboration in programming languages that is close to formal specification and hence allows for analysis of semantics of the language. We demonstrate the approach on two case studies; we describe a novel, proof-relevant approach to type inference and term synthesis in dependently types languages and we show how proof-relevant resolution allows for analysis of inductive and coinductive soundness of type class resolution. We conclude by a discussion of overall contributions of our current work.
Cite as

Frantisek Farka. Proof-Relevant Resolution for Elaboration of Programming Languages. In Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018). Open Access Series in Informatics (OASIcs), Volume 64, pp. 18:1-18:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{farka:OASIcs.ICLP.2018.18,
  author =	{Farka, Frantisek},
  title =	{{Proof-Relevant Resolution for Elaboration of Programming Languages}},
  booktitle =	{Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)},
  pages =	{18:1--18:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-090-3},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{64},
  editor =	{Dal Palu', Alessandro and Tarau, Paul and Saeedloei, Neda and Fodor, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2018.18},
  URN =		{urn:nbn:de:0030-drops-98848},
  doi =		{10.4230/OASIcs.ICLP.2018.18},
  annote =	{Keywords: resolution, elaboration, proof-relevant, dependent types, type classes}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.27
An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity

Authors: Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
This study considers the soft capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing vertex-weighted graph G=(V,E), which allows edge insertions and edge deletions, the goal is to design a data structure that maintains an approximate minimum vertex cover while satisfying the capacity constraint of each vertex. That is, when picking a copy of a vertex v in the cover, the number of v's incident edges covered by the copy is up to a given capacity of v. We extend Bhattacharya et al.'s work [SODA'15 and ICALP'15] to obtain a deterministic primal-dual algorithm for maintaining a constant-factor approximate minimum capacitated vertex cover with O(log n / epsilon) amortized update time, where n is the number of vertices in the graph. The algorithm can be extended to (1) a more general model in which each edge is associated with a non-uniform and unsplittable demand, and (2) the more general capacitated set cover problem.
Cite as

Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane. An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{wei_et_al:LIPIcs.APPROX-RANDOM.2018.27,
  author =	{Wei, Hao-Ting and Hon, Wing-Kai and Horn, Paul and Liao, Chung-Shou and Sadakane, Kunihiko},
  title =	{{An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  URN =		{urn:nbn:de:0030-drops-94312},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  annote =	{Keywords: approximation algorithm, dynamic algorithm, primal-dual, vertex cover}
}
Document
DOI: 10.4230/OASIcs.ICLP.2017.10
A Hitchhiker's Guide to Reinventing a Prolog Machine

Authors: Paul Tarau

Published in: OASIcs, Volume 58, Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017)

Abstract
We take a fresh, "clean-room" look at implementing Prolog by deriving its translation to an executable representation and its execution algorithm from a simple Horn Clause meta-interpreter. The resulting design has some interesting properties. The heap representation of terms and the abstract machine instruction encodings are the same. No dedicated code area is used as the code is placed directly on the heap. Unification and indexing operations are orthogonal. Filtering of matching clauses happens without building new structures on the heap. Variables in function and predicate symbol positions are handled with no performance penalty. A simple English-like syntax is used as an intermediate representation for clauses and goals and the same simple syntax can be used by programmers directly as an alternative to classic Prolog syntax. Solutions of (multiple) logic engines are exposed as answer streams that can be combined through typical functional programming patterns, with flexibility to stop, resume, encapsulate and interleave executions. Performance of a basic interpreter implementing our design is within a factor of 2 of a highly optimized compiled WAM-based system using the same host language. To help placing our design on the fairly rich map of Prolog systems, we discuss similarities to existing Prolog abstract machines, with emphasis on separating necessary commonalities from arbitrary implementation choices.
Cite as

Paul Tarau. A Hitchhiker's Guide to Reinventing a Prolog Machine. In Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017). Open Access Series in Informatics (OASIcs), Volume 58, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{tarau:OASIcs.ICLP.2017.10,
  author =	{Tarau, Paul},
  title =	{{A Hitchhiker's Guide to Reinventing a Prolog Machine}},
  booktitle =	{Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017)},
  pages =	{10:1--10:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-058-3},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{58},
  editor =	{Rocha, Ricardo and Son, Tran Cao and Mears, Christopher and Saeedloei, Neda},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2017.10},
  URN =		{urn:nbn:de:0030-drops-84537},
  doi =		{10.4230/OASIcs.ICLP.2017.10},
  annote =	{Keywords: Prolog abstract machines, heap representation of terms and code, immutable goal stacks, natural language syntax for clauses, answer streams, multi-arg}
}
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