56 Search Results for "Schmidt-Schauß, Manfred"

Volume

OASIcs, Volume 46

2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)

WPTE 2015, July 2, 2015, Warsaw, Poland

Editors: Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß

Volume

OASIcs, Volume 40

First International Workshop on Rewriting Techniques for Program Transformations and Evaluation

WPTE 2014, July 13, 2014, Vienna, Austria

Editors: Manfred Schmidt-Schauß, Masahiko Sakai, David Sabel, and Yuki Chiba

Volume

LIPIcs, Volume 10

22nd International Conference on Rewriting Techniques and Applications (RTA'11)

RTA 2011, May 30 to June 1, 2011, Novi Sad, Serbia

Editors: Manfred Schmidt-Schauss

Document
DOI: 10.4230/LIPIcs.ITP.2025.12
Automatically Generalizing Proofs and Statements

Authors: Anshula Gandhi, Anand Rao Tadipatri, and Timothy Gowers

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

Abstract
We present an algorithm, developed in the Lean programming language, to automatically generalize mathematical proofs. The algorithm, which builds on work by Olivier Pons, advances state-of-the-art proof generalization by robustly generalizing repeated and related constants, as well as abstracting out hypotheses implicitly concerning them. We also discuss the role of proof generalization in conjecturing, learning from failure, and other aspects of mathematical proof discovery.
Cite as

Anshula Gandhi, Anand Rao Tadipatri, and Timothy Gowers. Automatically Generalizing Proofs and Statements. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gandhi_et_al:LIPIcs.ITP.2025.12,
  author =	{Gandhi, Anshula and Tadipatri, Anand Rao and Gowers, Timothy},
  title =	{{Automatically Generalizing Proofs and Statements}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{12:1--12:18},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-246104},
  doi =		{10.4230/LIPIcs.ITP.2025.12},
  annote =	{Keywords: automated reasoning, automated theorem proving, interactive theorem proving, formalization of mathematics, generalization, Lean theorem prover, Lean tactic}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.69
FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree

Authors: Markus Lohrey, Sebastian Maneth, and Markus L. Schmid

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the structure is given in a potentially highly compressed form by a straight-line program (SLP). Our main result is an algorithm that enumerates the result set of a first-order query over a structure of bounded degree that is represented by an SLP satisfying the so-called apex condition. For a fixed formula, the enumeration algorithm has constant delay and needs a preprocessing time that is linear in the size of the SLP.
Cite as

Markus Lohrey, Sebastian Maneth, and Markus L. Schmid. FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2025.69,
  author =	{Lohrey, Markus and Maneth, Sebastian and Schmid, Markus L.},
  title =	{{FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.69},
  URN =		{urn:nbn:de:0030-drops-241760},
  doi =		{10.4230/LIPIcs.MFCS.2025.69},
  annote =	{Keywords: Enumeration algorithms, FO-logic, query evaluation over compressed data}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.5
The Cost of Skeletal Call-By-Need, Smoothly

Authors: Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen

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

Abstract
Skeletal call-by-need is an optimization of call-by-need evaluation also known as "fully lazy sharing": when the duplication of a value has to take place, it is first split into "skeleton", which is then duplicated, and "flesh" which is instead kept shared. Here, we provide two cost analyses of skeletal call-by-need. Firstly, we provide a family of terms showing that skeletal call-by-need can be asymptotically exponentially faster than call-by-need in both time and space; it is the first such evidence, to our knowledge. Secondly, we prove that skeletal call-by-need can be implemented efficiently, that is, with bi-linear overhead. This result is obtained by providing a new smooth presentation of ideas by Shivers and Wand for the reconstruction of skeletons, which is then smoothly plugged into the study of an abstract machine following the distillation technique by Accattoli et al.
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Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen. The Cost of Skeletal Call-By-Need, Smoothly. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2025.5,
  author =	{Accattoli, Beniamino and Magliocca, Francesco and Peyrot, Lo\"{i}c and Sacerdoti Coen, Claudio},
  title =	{{The Cost of Skeletal Call-By-Need, Smoothly}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{5:1--5:22},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-236206},
  doi =		{10.4230/LIPIcs.FSCD.2025.5},
  annote =	{Keywords: \lambda-calculus, abstract machines, call-by-need, cost models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.7
Combining Generalization Algorithms in Regular Collapse-Free Theories

Authors: Mauricio Ayala-Rincón, David M. Cerna, Temur Kutsia, and Christophe Ringeissen

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

Abstract
We look at the generalization problem modulo some equational theories. This problem is dual to the unification problem: given two input terms, we want to find a common term whose respective two instances are equivalent to the original terms modulo the theory. There exist algorithms for finding generalizations over various equational theories. We focus on modular construction of equational generalization algorithms for the union of signature-disjoint theories. Specifically, we consider the class of regular and collapse-free theories, showing how to combine existing generalization algorithms to produce specific solutions in these cases. Additionally, we identify a class of theories that admit a generalization algorithm based on the application of axioms to resolve the problem. To define this class, we rely on the notion of syntactic theories, a concept originally introduced to develop unification procedures similar to the one known for syntactic unification. We demonstrate that syntactic theories are also helpful in developing generalization procedures similar to those used for syntactic generalization.
Cite as

Mauricio Ayala-Rincón, David M. Cerna, Temur Kutsia, and Christophe Ringeissen. Combining Generalization Algorithms in Regular Collapse-Free Theories. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ayalarincon_et_al:LIPIcs.FSCD.2025.7,
  author =	{Ayala-Rinc\'{o}n, Mauricio and Cerna, David M. and Kutsia, Temur and Ringeissen, Christophe},
  title =	{{Combining Generalization Algorithms in Regular Collapse-Free Theories}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{7:1--7:18},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-236228},
  doi =		{10.4230/LIPIcs.FSCD.2025.7},
  annote =	{Keywords: Generalization, Anti-unification, Equational theories, Combination}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.8
The Unification Type of an Equational Theory May Depend on the Instantiation Preorder

Authors: Franz Baader and Oliver Fernández Gil

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

Abstract
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that all variables are considered. It has been known for more than three decades that the unification type of an equational theory may vary, depending on which instantiation preorder is used. More precisely, it was shown in 1991 that the theory ACUI of an associative, commutative, and idempotent binary function symbol with a unit is unitary w.r.t. the restricted instantiation preorder, but not unitary w.r.t. the unrestricted one. In 2016 this result was strengthened by showing that the unrestricted type of this theory also cannot be finitary. Here, we considerably improve on this result by proving that ACUI is infinitary w.r.t. the unrestricted instantiation preorder, thus precluding type zero. We also show that, w.r.t. this preorder, the unification type of ACU (where idempotency is removed from the axioms) and of AC (where additionally the unit is removed) is infinitary, though it is respectively unitary and finitary in the restricted case. In the other direction, we prove (using the example of unification in the description logic EL) that the unification type may actually improve from type zero to infinitary when switching from the restricted instantiation preorder to the unrestricted one. In addition, we establish some general results on the relationship between the two instantiation preorders.
Cite as

Franz Baader and Oliver Fernández Gil. The Unification Type of an Equational Theory May Depend on the Instantiation Preorder. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baader_et_al:LIPIcs.FSCD.2025.8,
  author =	{Baader, Franz and Fern\'{a}ndez Gil, Oliver},
  title =	{{The Unification Type of an Equational Theory May Depend on the Instantiation Preorder}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{8:1--8:24},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-236230},
  doi =		{10.4230/LIPIcs.FSCD.2025.8},
  annote =	{Keywords: Unification type, Instantiation preorder, Equational theories, Modal and Description Logics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.18
Knowledge Problems vs Unification and Matching: Dichotomy Results

Authors: Serdar Erbatur, Andrew M. Marshall, Paliath Narendran, and Christophe Ringeissen

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

Abstract
The research area of cryptographic protocol analysis contains a number of innovative algorithms and procedures for checking various security properties of protocols. Most of these procedures focus on solving one of several "knowledge problems" that model intruder knowledge. Solving these problems can demonstrate the ability of the intruder to obtain some forbidden information of the protocol, such as secret keys. Two important examples of these problems are the deduction problem and the static equivalence problem. Deduction is concerned with the ability to derive a term from a set of terms (or knowledge) obtained from the observation of a protocol instance. Static equivalence, on the other hand, is concerned with distinguishing between two runs of a protocol based on two sets of knowledge. These two knowledge problems at first inspection appear to be very close to the older automated reasoning problems of matching and unification. However, this first impression is wrong, and there have been a few results that have shown theories where one problem, such as unification, is undecidable but another problem, such as deduction, is decidable. These existing dichotomy results were, however, incomplete, and not all cases had been examined, thus leaving the possibility of some connection between the problems for those unexamined cases. In this paper, we consider the missing dichotomy cases. For each of the remaining cases, we demonstrate a theory that separates the two problems. In addition, once the dichotomy results are completed, it leaves open the question of the existence of non-trivial classes of theories for which all four of the problems are decidable. One example for which this is true is the well-known class of subterm convergent term rewrite systems. In this paper, we develop another example, a class of restrictive permutative theories for which all problems are likewise decidable.
Cite as

Serdar Erbatur, Andrew M. Marshall, Paliath Narendran, and Christophe Ringeissen. Knowledge Problems vs Unification and Matching: Dichotomy Results. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erbatur_et_al:LIPIcs.FSCD.2025.18,
  author =	{Erbatur, Serdar and Marshall, Andrew M. and Narendran, Paliath and Ringeissen, Christophe},
  title =	{{Knowledge Problems vs Unification and Matching: Dichotomy Results}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{18:1--18:17},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-236331},
  doi =		{10.4230/LIPIcs.FSCD.2025.18},
  annote =	{Keywords: Knowledge Problems, Unification, Matching, Decidability}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.4
Logics for Conceptual Data Modelling: A Review

Authors: Pablo R. Fillottrani and C. Maria Keet

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Information modelling for databases and object-oriented information systems avails of conceptual data modelling languages such as EER and UML Class Diagrams. Many attempts exist to add logical rigour to them, for various reasons and with disparate strengths. In this paper we aim to provide a structured overview of the many efforts. We focus on aims, approaches to the formalisation, including key dimensions of choice points, popular logics used, and the main relevant reasoning services. We close with current challenges and research directions.
Cite as

Pablo R. Fillottrani and C. Maria Keet. Logics for Conceptual Data Modelling: A Review. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 4:1-4:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{fillottrani_et_al:TGDK.2.1.4,
  author =	{Fillottrani, Pablo R. and Keet, C. Maria},
  title =	{{Logics for Conceptual Data Modelling: A Review}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:30},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.4},
  URN =		{urn:nbn:de:0030-drops-198616},
  doi =		{10.4230/TGDK.2.1.4},
  annote =	{Keywords: Conceptual Data Modelling, EER, UML, Description Logics, OWL}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.7
Nominal Anti-Unification with Atom-Variables

Authors: Manfred Schmidt-Schauß and Daniele Nantes-Sobrinho

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Anti-unification is the task of generalizing a set of expressions in the most specific way. It was extended to the nominal framework by Baumgarter, Kutsia, Levy and Villaret, who defined an algorithm solving the nominal anti-unification problem, which runs in polynomial time. Unfortunately, when an infinite set of atoms are allowed in generalizations, a minimal complete set of solutions in nominal anti-unification does not exist, in general. In this paper, we present a more general approach to nominal anti-unification that uses atom-variables instead of explicit atoms, and two variants of freshness constraints: NL_A-constraints (with atom-variables), and Eqr-constraints based on Equivalence relations on atom-variables. The idea of atom-variables is that different atom-variables may be instantiated with identical or different atoms. Albeit simple, this freedom in the formulation increases its application potential: we provide an algorithm that is finitary for the NL_A-freshness constraints, and for Eqr-freshness constraints it computes a unique least general generalization. There is a price to pay in the general case: checking freshness constraints and other related logical questions will require exponential time. The setting of Baumgartner et al. is improved by the atom-only case, which runs in polynomial time and computes a unique least general generalization.
Cite as

Manfred Schmidt-Schauß and Daniele Nantes-Sobrinho. Nominal Anti-Unification with Atom-Variables. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schmidtschau_et_al:LIPIcs.FSCD.2022.7,
  author =	{Schmidt-Schau{\ss}, Manfred and Nantes-Sobrinho, Daniele},
  title =	{{Nominal Anti-Unification with Atom-Variables}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.7},
  URN =		{urn:nbn:de:0030-drops-162885},
  doi =		{10.4230/LIPIcs.FSCD.2022.7},
  annote =	{Keywords: Generalization, anti-unification, nominal algorithms, higher-order deduction}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.28
Nominal Unification with Atom and Context Variables

Authors: Manfred Schmidt-Schauß and David Sabel

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
Automated deduction in higher-order program calculi, where properties of transformation rules are demanded, or confluence or other equational properties are requested, can often be done by syntactically computing overlaps (critical pairs) of reduction rules and transformation rules. Since higher-order calculi have alpha-equivalence as fundamental equivalence, the reasoning procedure must deal with it. We define ASD1-unification problems, which are higher-order equational unification problems employing variables for atoms, expressions and contexts, with additional distinct-variable constraints, and which have to be solved w.r.t. alpha-equivalence. Our proposal is to extend nominal unification to solve these unification problems. We succeeded in constructing the nominal unification algorithm NomUnifyASD. We show that NomUnifyASD is sound and complete for this problem class, and outputs a set of unifiers with constraints in nondeterministic polynomial time if the final constraints are satisfiable. We also show that solvability of the output constraints can be decided in NEXPTIME, and for a fixed number of context-variables in NP time. For terms without context-variables and atom-variables, NomUnifyASD runs in polynomial time, is unitary, and extends the classical problem by permitting distinct-variable constraints.
Cite as

Manfred Schmidt-Schauß and David Sabel. Nominal Unification with Atom and Context Variables. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{schmidtschau_et_al:LIPIcs.FSCD.2018.28,
  author =	{Schmidt-Schau{\ss}, Manfred and Sabel, David},
  title =	{{Nominal Unification with Atom and Context Variables}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.28},
  URN =		{urn:nbn:de:0030-drops-91983},
  doi =		{10.4230/LIPIcs.FSCD.2018.28},
  annote =	{Keywords: automated deduction, nominal unification, lambda calculus, functional programming}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.405
Two-Restricted One Context Unification is in Polynomial Time

Authors: Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari

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

Abstract
One Context Unification (1CU) extends first-order unification by introducing a single context variable. This problem was recently shown to be in NP, but it is not known to be solvable in polynomial time. We show that the case of 1CU where the context variable occurs at most twice in the input (1CU2r) is solvable in polynomial time. Moreover, a polynomial representation of all solutions can also be computed in polynomial time. The 1CU2r problem is important as it is used as a subroutine in polynomial time algorithms for several more-general classes of 1CU problem. Our algorithm can be seen as an extension of the usual rules of first-order unification and can be used to solve related problems in polynomial time, such as first-order unification of two terms that tolerates one clash. All our results assume that the input terms are represented as Directed Acyclic Graphs.
Cite as

Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari. Two-Restricted One Context Unification is in Polynomial Time. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 405-422, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{gascon_et_al:LIPIcs.CSL.2015.405,
  author =	{Gasc\'{o}n, Adri\`{a} and Schmidt-Schau{\ss}, Manfred and Tiwari, Ashish},
  title =	{{Two-Restricted One Context Unification is in Polynomial Time}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{405--422},
  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.2015.405},
  URN =		{urn:nbn:de:0030-drops-54289},
  doi =		{10.4230/LIPIcs.CSL.2015.405},
  annote =	{Keywords: context unification, first-order unification, deduction, type checking}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.WPTE.2015
OASIcs, Volume 46, WPTE'15, Complete Volume

Authors: Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß

Published in: OASIcs, Volume 46, 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)

Abstract
OASIcs, Volume 46, WPTE'15, Complete Volume
Cite as

2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015). Open Access Series in Informatics (OASIcs), Volume 46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@Proceedings{chiba_et_al:OASIcs.WPTE.2015,
  title =	{{OASIcs, Volume 46, WPTE'15, Complete Volume}},
  booktitle =	{2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-94-1},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{46},
  editor =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2015},
  URN =		{urn:nbn:de:0030-drops-52644},
  doi =		{10.4230/OASIcs.WPTE.2015},
  annote =	{Keywords: Conference proceedings, Concurrent Programming, Formal Definitions and Theory, Specifying and Verifying and Reasoning about Programs, Semantics of Programming Languages, Mathematical Logic, Grammars and Other Rewriting Systems, Deduction and Theorem Proving}
}
Document
Front Matter
DOI: 10.4230/OASIcs.WPTE.2015.i
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß

Published in: OASIcs, Volume 46, 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)

Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
Cite as

2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015). Open Access Series in Informatics (OASIcs), Volume 46, pp. i-xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{chiba_et_al:OASIcs.WPTE.2015.i,
  author =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)},
  pages =	{i--xvi},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-94-1},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{46},
  editor =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2015.i},
  URN =		{urn:nbn:de:0030-drops-51765},
  doi =		{10.4230/OASIcs.WPTE.2015.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
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