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Documents authored by Rubin, Sasha

Document
DOI: 10.4230/LIPIcs.CSL.2018.23
Quantifying Bounds in Strategy Logic

Authors: Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Sasha Rubin

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

Abstract
Program synthesis constructs programs from specifications in an automated way. Strategy Logic (SL) is a powerful and versatile specification language whose goal is to give theoretical foundations for program synthesis in a multi-agent setting. One limitation of Strategy Logic is that it is purely qualitative. For instance it cannot specify quantitative properties of executions such as "every request is quickly granted", or quantitative properties of trees such as "most executions of the system terminate". In this work, we extend Strategy Logic to include quantitative aspects in a way that can express bounds on "how quickly" and "how many". We define Prompt Strategy Logic, which encompasses Prompt LTL (itself an extension of LTL with a prompt eventuality temporal operator), and we define Bounded-Outcome Strategy Logic which has a bounded quantifier on paths. We supply a general technique, based on the study of automata with counters, that solves the model-checking problems for both these logics.
Cite as

Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Sasha Rubin. Quantifying Bounds in Strategy Logic. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fijalkow_et_al:LIPIcs.CSL.2018.23,
  author =	{Fijalkow, Nathana\"{e}l and Maubert, Bastien and Murano, Aniello and Rubin, Sasha},
  title =	{{Quantifying Bounds in Strategy Logic}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{23:1--23:23},
  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.2018.23},
  URN =		{urn:nbn:de:0030-drops-96901},
  doi =		{10.4230/LIPIcs.CSL.2018.23},
  annote =	{Keywords: Prompt LTL, Strategy Logic, Model checking, Automata with counters}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1353
Order-Invariant MSO is Stronger than Counting MSO in the Finite

Authors: Tobias Ganzow and Sasha Rubin

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

Abstract
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers, allowing the expression of queries like ``the number of elements in the structure is even''. The second extension allows the use of an additional binary predicate, not contained in the signature of the queried structure, that must be interpreted as an arbitrary linear order on its universe, obtaining order-invariant MSO. While it is straightforward that every CMSO formula can be translated into an equivalent order-invariant MSO formula, the converse had not yet been settled. Courcelle showed that for restricted classes of structures both order-invariant MSO and CMSO are equally expressive, but conjectured that, in general, order-invariant MSO is stronger than CMSO. We affirm this conjecture by presenting a class of structures that is order-invariantly definable in MSO but not definable in CMSO.
Cite as

Tobias Ganzow and Sasha Rubin. Order-Invariant MSO is Stronger than Counting MSO in the Finite. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 313-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{ganzow_et_al:LIPIcs.STACS.2008.1353,
  author =	{Ganzow, Tobias and Rubin, Sasha},
  title =	{{Order-Invariant MSO is Stronger than Counting MSO in the Finite}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{313--324},
  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.2008.1353},
  URN =		{urn:nbn:de:0030-drops-13535},
  doi =		{10.4230/LIPIcs.STACS.2008.1353},
  annote =	{Keywords: MSO, Counting MSO, order-invariance, expressiveness, Ehrenfeucht-Fraiss\'{e} game}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1360
Cardinality and counting quantifiers on omega-automatic structures

Authors: Lukasz Kaiser, Sasha Rubin, and Vince Bárány

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

Abstract
We investigate structures that can be represented by omega-automata, so called omega-automatic structures, and prove that relations defined over such structures in first-order logic expanded by the first-order quantifiers `there exist at most $aleph_0$ many', 'there exist finitely many' and 'there exist $k$ modulo $m$ many' are omega-regular. The proof identifies certain algebraic properties of omega-semigroups. As a consequence an omega-regular equivalence relation of countable index has an omega-regular set of representatives. This implies Blumensath's conjecture that a countable structure with an $omega$-automatic presentation can be represented using automata on finite words. This also complements a very recent result of Hj"orth, Khoussainov, Montalban and Nies showing that there is an omega-automatic structure which has no injective presentation.
Cite as

Lukasz Kaiser, Sasha Rubin, and Vince Bárány. Cardinality and counting quantifiers on omega-automatic structures. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 385-396, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kaiser_et_al:LIPIcs.STACS.2008.1360,
  author =	{Kaiser, Lukasz and Rubin, Sasha and B\'{a}r\'{a}ny, Vince},
  title =	{{Cardinality and counting quantifiers on omega-automatic structures}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{385--396},
  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.2008.1360},
  URN =		{urn:nbn:de:0030-drops-13602},
  doi =		{10.4230/LIPIcs.STACS.2008.1360},
  annote =	{Keywords: \$omega\$-automatic presentations, \$omega\$-semigroups, \$omega\$-automata}
}
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