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Documents authored by Kuske, Dietrich

Document
DOI: 10.4230/LIPIcs.STACS.2024.12
Modal Logic Is More Succinct Iff Bi-Implication Is Available in Some Form

Authors: Christoph Berkholz, Dietrich Kuske, and Christian Schwarz

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
Is it possible to write significantly smaller formulae, when using more Boolean operators in addition to the De Morgan basis (and, or, not)? For propositional logic a negative answer was given by Pratt: every formula with additional operators can be translated to the De Morgan basis with only polynomial increase in size. Surprisingly, for modal logic the picture is different: we show that adding bi-implication allows to write exponentially smaller formulae. Moreover, we provide a complete classification of finite sets of Boolean operators showing they are either of no help (allow polynomial translations to the De Morgan basis) or can express properties as succinct as modal logic with additional bi-implication. More precisely, these results are shown for the modal logic T (and therefore for K). We complement this result showing that the modal logic S5 behaves as propositional logic: no additional Boolean operators make it possible to write significantly smaller formulae.
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Christoph Berkholz, Dietrich Kuske, and Christian Schwarz. Modal Logic Is More Succinct Iff Bi-Implication Is Available in Some Form. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berkholz_et_al:LIPIcs.STACS.2024.12,
  author =	{Berkholz, Christoph and Kuske, Dietrich and Schwarz, Christian},
  title =	{{Modal Logic Is More Succinct Iff Bi-Implication Is Available in Some Form}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.12},
  URN =		{urn:nbn:de:0030-drops-197228},
  doi =		{10.4230/LIPIcs.STACS.2024.12},
  annote =	{Keywords: succinctness, modal logic}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.20
A Class of Rational Trace Relations Closed Under Composition

Authors: Dietrich Kuske

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
Rational relations on words form a well-studied and often applied notion. While the definition in trace monoids is immediate, they have not been studied in this more general context. A possible reason is that they do not share the main useful properties of rational relations on words. To overcome this unfortunate limitation, this paper proposes a restricted class of rational relations, investigates its properties, and applies the findings to systems equipped with a pushdown that does not hold a word but a trace.
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Dietrich Kuske. A Class of Rational Trace Relations Closed Under Composition. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kuske:LIPIcs.FSTTCS.2023.20,
  author =	{Kuske, Dietrich},
  title =	{{A Class of Rational Trace Relations Closed Under Composition}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.20},
  URN =		{urn:nbn:de:0030-drops-193935},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.20},
  annote =	{Keywords: rational relations, Mazurkiewicz traces, preservation of rationality and recognizability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.61
Complexity of Counting First-Order Logic for the Subword Order

Authors: Dietrich Kuske and Christian Schwarz

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
This paper considers the structure consisting of the set of all words over a given alphabet together with the subword relation, regular predicates, and constants for every word. We are interested in the counting extension of first-order logic by threshold counting quantifiers. The main result shows that the two-variable fragment of this logic can be decided in two-fold exponential space provided the regular predicates are restricted to piecewise testable ones. This result improves prior insights by Karandikar and Schnoebelen by extending the logic and saving one exponent. Its proof consists of two main parts: First, we provide a quantifier elimination procedure that results in a formula with constants of bounded length (this generalizes the procedure by Karandikar and Schnoebelen for first-order logic). From this, it follows that quantification in formulas can be restricted to words of bounded length, i.e., the second part of the proof is an adaptation of the method by Ferrante and Rackoff to counting logic and deviates significantly from the path of reasoning by Karandikar and Schnoebelen.
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Dietrich Kuske and Christian Schwarz. Complexity of Counting First-Order Logic for the Subword Order. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kuske_et_al:LIPIcs.MFCS.2020.61,
  author =	{Kuske, Dietrich and Schwarz, Christian},
  title =	{{Complexity of Counting First-Order Logic for the Subword Order}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{61:1--61:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.61},
  URN =		{urn:nbn:de:0030-drops-127297},
  doi =		{10.4230/LIPIcs.MFCS.2020.61},
  annote =	{Keywords: Counting logic, piecewise testable languages}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.3
Climbing up the Elementary Complexity Classes with Theories of Automatic Structures

Authors: Faried Abu Zaid, Dietrich Kuske, and Peter Lindner

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Automatic structures are structures that admit a finite presentation via automata. Their most prominent feature is that their theories are decidable. In the literature, one finds automatic structures with non-elementary theory (e.g., the complete binary tree with equal-level predicate) and automatic structures whose theories are at most 3-fold exponential (e.g., Presburger arithmetic or infinite automatic graphs of bounded degree). This observation led Durand-Gasselin to the question whether there are automatic structures of arbitrary high elementary complexity. We give a positive answer to this question. Namely, we show that for every h >=0 the forest of (infinitely many copies of) all finite trees of height at most h+2 is automatic and it's theory is complete for STA(*, exp_h(n, poly(n)), poly(n)), an alternating complexity class between h-fold exponential time and space. This exact determination of the complexity of the theory of these forests might be of independent interest.
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Faried Abu Zaid, Dietrich Kuske, and Peter Lindner. Climbing up the Elementary Complexity Classes with Theories of Automatic Structures. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abuzaid_et_al:LIPIcs.CSL.2018.3,
  author =	{Abu Zaid, Faried and Kuske, Dietrich and Lindner, Peter},
  title =	{{Climbing up the Elementary Complexity Classes with Theories of Automatic Structures}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.3},
  URN =		{urn:nbn:de:0030-drops-96701},
  doi =		{10.4230/LIPIcs.CSL.2018.3},
  annote =	{Keywords: Automatic Structures, Complexity Theory, Model Theory}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.133
Gaifman Normal Forms for Counting Extensions of First-Order Logic

Authors: Dietrich Kuske and Nicole Schweikardt

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We consider the extension of first-order logic FO by unary counting quantifiers and generalise the notion of Gaifman normal form from FO to this setting. For formulas that use only ultimately periodic counting quantifiers, we provide an algorithm that computes equivalent formulas in Gaifman normal form. We also show that this is not possible for formulas using at least one quantifier that is not ultimately periodic. Now let d be a degree bound. We show that for any formula phi with arbitrary counting quantifiers, there is a formula gamma in Gaifman normal form that is equivalent to phi on all finite structures of degree <= d. If the quantifiers of phi are decidable (decidable in elementary time, ultimately periodic), gamma can be constructed effectively (in elementary time, in worst-case optimal 3-fold exponential time). For the setting with unrestricted degree we show that by using our Gaifman normal form for formulas with only ultimately periodic counting quantifiers, a known fixed-parameter tractability result for FO on classes of structures of bounded local tree-width can be lifted to the extension of FO with ultimately periodic counting quantifiers (a logic equally expressive as FO+MOD, i.e., first-oder logic with modulo-counting quantifiers).
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Dietrich Kuske and Nicole Schweikardt. Gaifman Normal Forms for Counting Extensions of First-Order Logic. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 133:1-133:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kuske_et_al:LIPIcs.ICALP.2018.133,
  author =	{Kuske, Dietrich and Schweikardt, Nicole},
  title =	{{Gaifman Normal Forms for Counting Extensions of First-Order Logic}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{133:1--133:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.133},
  URN =		{urn:nbn:de:0030-drops-91375},
  doi =		{10.4230/LIPIcs.ICALP.2018.133},
  annote =	{Keywords: Finite model theory, Gaifman locality, modulo-counting quantifiers, fixed parameter tractable model-checking}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.472
Infinite and Bi-infinite Words with Decidable Monadic Theories

Authors: Dietrich Kuske, Jiamou Liu, and Anastasia Moskvina

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

Abstract
We study word structures of the form (D,<=,P) where D is either N or Z, <= is a linear ordering on D and P in D is a predicate on D. In particular we show: (a) The set of recursive omega-words with decidable monadic second order theories is Sigma_3-complete. (b) We characterise those sets P subset of Z that yield bi-infinite words (Z,<=,P) with decidable monadic second order theories. (c) We show that such "tame" predicates P exist in every Turing degree. (d) We determine, for P subset of Z, the number of predicates Q subset of Z such that (Z,<=,P) and (Z,<=,Q) are indistinguishable. Through these results we demonstrate similarities and differences between logical properties of infinite and bi-infinite words.
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Dietrich Kuske, Jiamou Liu, and Anastasia Moskvina. Infinite and Bi-infinite Words with Decidable Monadic Theories. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 472-486, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kuske_et_al:LIPIcs.CSL.2015.472,
  author =	{Kuske, Dietrich and Liu, Jiamou and Moskvina, Anastasia},
  title =	{{Infinite and Bi-infinite Words with Decidable Monadic Theories}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{472--486},
  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.2015.472},
  URN =		{urn:nbn:de:0030-drops-54325},
  doi =		{10.4230/LIPIcs.CSL.2015.472},
  annote =	{Keywords: infinite words, bi-infinite words, monadic second order logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.455
Isomorphisms of scattered automatic linear orders

Authors: Dietrich Kuske

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
We prove the undecidability of the existence of an isomorphism between scattered tree-automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders. For the existence of automatic automorphisms of word automatic linear orders, we determine the exact level of undecidability in the arithmetical hierarchy.
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Dietrich Kuske. Isomorphisms of scattered automatic linear orders. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 455-469, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{kuske:LIPIcs.CSL.2012.455,
  author =	{Kuske, Dietrich},
  title =	{{Isomorphisms of scattered automatic linear orders}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{455--469},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.455},
  URN =		{urn:nbn:de:0030-drops-36906},
  doi =		{10.4230/LIPIcs.CSL.2012.455},
  annote =	{Keywords: Automatic structures, isomorphism, automorphism}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2483
Is Ramsey's Theorem omega-automatic?

Authors: Dietrich Kuske

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We study the existence of infinite cliques in $\omega$-automatic (hyper-)graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifically, we show that every uncountable $\omega$-automatic graph contains an uncountable co-context-free clique or anticlique, but not necessarily a context-free (let alone regular) clique or anticlique. We also show that uncountable $\omega$-automatic ternary hypergraphs need not have uncountable cliques or anticliques at all.
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Dietrich Kuske. Is Ramsey's Theorem omega-automatic?. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 537-548, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{kuske:LIPIcs.STACS.2010.2483,
  author =	{Kuske, Dietrich},
  title =	{{Is Ramsey's Theorem omega-automatic?}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{537--548},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2483},
  URN =		{urn:nbn:de:0030-drops-24838},
  doi =		{10.4230/LIPIcs.STACS.2010.2483},
  annote =	{Keywords: Logic in computer science, automata, Ramsey theory}
}
Document
DOI: 10.4230/DagSemProc.07441.1
07441 Abstracts Collection – Algorithmic-Logical Theory of Infinite Structures

Authors: Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi

Published in: Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

Abstract
From 28.10. to 02.11.2007, the Dagstuhl Seminar 07441 ``Algorithmic-Logical Theory of Infinite Structures'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi. 07441 Abstracts Collection – Algorithmic-Logical Theory of Infinite Structures. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{downey_et_al:DagSemProc.07441.1,
  author =	{Downey, Rod and Khoussainov, Bakhadyr and Kuske, Dietrich and Lohrey, Markus and Vardi, Moshe Y.},
  title =	{{07441 Abstracts Collection – Algorithmic-Logical Theory of Infinite Structures}},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7441},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.1},
  URN =		{urn:nbn:de:0030-drops-14122},
  doi =		{10.4230/DagSemProc.07441.1},
  annote =	{Keywords: Theories of infinite structures , computable model theory and automatic structures , model checking infinite systems}
}
Document
DOI: 10.4230/DagSemProc.07441.2
07441 Summary – Algorithmic-Logical Theory of Infinite Structures

Authors: Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi

Published in: Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

Abstract
One of the important research fields of theoretical and applied computer science and mathematics is the study of algorithmic, logical and model theoretic properties of structures and their interactions. By a structure we mean typical objects that arise in computer science and mathematics such as data structures, programs, transition systems, graphs, large databases, XML documents, algebraic systems including groups, integers, fields, Boolean algebras and so on.
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Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi. 07441 Summary – Algorithmic-Logical Theory of Infinite Structures. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{downey_et_al:DagSemProc.07441.2,
  author =	{Downey, Rod and Khoussainov, Bakhadyr and Kuske, Dietrich and Lohrey, Markus and Vardi, Moshe Y.},
  title =	{{07441 Summary – Algorithmic-Logical Theory of Infinite Structures}},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7441},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.2},
  URN =		{urn:nbn:de:0030-drops-14111},
  doi =		{10.4230/DagSemProc.07441.2},
  annote =	{Keywords: Theories of infinite structures , computable model theory and automatic structures , model checking infinite systems}
}
Document
DOI: 10.4230/DagSemProc.07441.4
Compatibility of Shelah and Stupp's and of Muchnik's iteration with fragments of monadic second order logic

Authors: Dietrich Kuske

Published in: Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

Abstract
We investigate the relation between the theory of the iterations in the sense of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for several logics. These logics are obtained from the restriction of set quantification in monadic second order logic to certain subsets like, e.g., finite sets, chains, and finite unions of chains. We show that these theories of the Shelah-Stupp iteration can be reduced to corresponding theories of the base structure. This fails for Muchnik's iteration.
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Dietrich Kuske. Compatibility of Shelah and Stupp's and of Muchnik's iteration with fragments of monadic second order logic. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kuske:DagSemProc.07441.4,
  author =	{Kuske, Dietrich},
  title =	{{Compatibility of Shelah and Stupp's and of Muchnik's iteration with fragments of monadic second order logic}},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7441},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.4},
  URN =		{urn:nbn:de:0030-drops-14078},
  doi =		{10.4230/DagSemProc.07441.4},
  annote =	{Keywords: Logic in computer science, Rabin's tree theorem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1366
Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic

Authors: Dietrich Kuske

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We investigate the relation between the theory of the iterations in the sense of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for several logics. These logics are obtained from the restriction of set quantification in monadic second order logic to certain subsets like, e.g., finite sets, chains, and finite unions of chains. We show that these theories of the Shelah-Stupp iteration can be reduced to corresponding theories of the base structure. This fails for Muchnik's iteration.
Cite as

Dietrich Kuske. Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 467-478, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kuske:LIPIcs.STACS.2008.1366,
  author =	{Kuske, Dietrich},
  title =	{{Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{467--478},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1366},
  URN =		{urn:nbn:de:0030-drops-13668},
  doi =		{10.4230/LIPIcs.STACS.2008.1366},
  annote =	{Keywords: Logic in computer science, Rabin's tree theorem}
}
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