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Documents authored by Hague, Matthew


Document
Optimal Strategies in Pushdown Reachability Games

Authors: Arnaud Carayol and Matthew Hague

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
An algorithm for computing optimal strategies in pushdown reachability games was given by Cachat. We show that the information tracked by this algorithm is too coarse and the strategies constructed are not necessarily optimal. We then show that the algorithm can be refined to recover optimality. Through a further non-trivial argument the refined algorithm can be run in 2EXPTIME by bounding the play-lengths tracked to those that are at most doubly exponential. This is optimal in the sense that there exists a game for which the optimal strategy requires a doubly exponential number of moves to reach a target configuration.

Cite as

Arnaud Carayol and Matthew Hague. Optimal Strategies in Pushdown Reachability Games. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 42:1-42:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{carayol_et_al:LIPIcs.MFCS.2018.42,
  author =	{Carayol, Arnaud and Hague, Matthew},
  title =	{{Optimal Strategies in Pushdown Reachability Games}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.42},
  URN =		{urn:nbn:de:0030-drops-96248},
  doi =		{10.4230/LIPIcs.MFCS.2018.42},
  annote =	{Keywords: Pushdown Systems, Reachability Games, Optimal Strategies, Formal Methods, Context Free}
}
Document
Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems

Authors: Matthew Hague, Roland Meyer, Sebastian Muskalla, and Martin Zimmermann

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known since both problems are complete for the same complexity class. Coming up with a direct reduction, however, has been an open problem. Our solution to the puzzle brings together a number of techniques for pushdown games and adds three new ones. This work contributes to a recent trend of liveness to safety reductions which allow the advanced state-of-the-art in safety checking to be used for more expressive specifications.

Cite as

Matthew Hague, Roland Meyer, Sebastian Muskalla, and Martin Zimmermann. Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 57:1-57:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{hague_et_al:LIPIcs.MFCS.2018.57,
  author =	{Hague, Matthew and Meyer, Roland and Muskalla, Sebastian and Zimmermann, Martin},
  title =	{{Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.57},
  URN =		{urn:nbn:de:0030-drops-96396},
  doi =		{10.4230/LIPIcs.MFCS.2018.57},
  annote =	{Keywords: Parity Games, Safety Games, Pushdown Systems, Collapsible Pushdown Systems, Higher-Order Recursion Schemes, Model Checking}
}
Document
Domains for Higher-Order Games

Authors: Matthew Hague, Roland Meyer, and Sebastian Muskalla

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)


Abstract
We study two-player inclusion games played over word-generating higher-order recursion schemes. While inclusion checks are known to capture verification problems, two-player games generalize this relationship to program synthesis. In such games, non-terminals of the grammar are controlled by opposing players. The goal of the existential player is to avoid producing a word that lies outside of a regular language of safe words. We contribute a new domain that provides a representation of the winning region of such games. Our domain is based on (functions over) potentially infinite Boolean formulas with words as atomic propositions. We develop an abstract interpretation framework that we instantiate to abstract this domain into a domain where the propositions are replaced by states of a finite automaton. This second domain is therefore finite and we obtain, via standard fixed-point techniques, a direct algorithm for the analysis of two-player inclusion games. We show, via a second instantiation of the framework, that our finite domain can be optimized, leading to a (k+1)EXP algorithm for order-k recursion schemes. We give a matching lower bound, showing that our approach is optimal. Since our approach is based on standard Kleene iteration, existing techniques and tools for fixed-point computations can be applied.

Cite as

Matthew Hague, Roland Meyer, and Sebastian Muskalla. Domains for Higher-Order Games. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 59:1-59:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{hague_et_al:LIPIcs.MFCS.2017.59,
  author =	{Hague, Matthew and Meyer, Roland and Muskalla, Sebastian},
  title =	{{Domains for Higher-Order Games}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{59:1--59:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.59},
  URN =		{urn:nbn:de:0030-drops-81409},
  doi =		{10.4230/LIPIcs.MFCS.2017.59},
  annote =	{Keywords: higher-order recursion schemes, games, semantics, abstract interpretation, fixed points}
}
Document
Saturation of Concurrent Collapsible Pushdown Systems

Authors: Matthew Hague

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)


Abstract
Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to decidability. To model higher-order procedures calls, a generalisation of pushdown stacks called collapsible pushdown stacks are required. Reachability problems for multi-stack collapsible pushdown systems have been little studied. Here, we study ordered, phase-bounded and scope-bounded multi-stack collapsible pushdown systems using saturation techniques, showing decidability of control state reachability and giving a regular representation of all configurations that can reach a given control state.

Cite as

Matthew Hague. Saturation of Concurrent Collapsible Pushdown Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 313-325, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{hague:LIPIcs.FSTTCS.2013.313,
  author =	{Hague, Matthew},
  title =	{{Saturation of Concurrent Collapsible Pushdown Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{313--325},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.313},
  URN =		{urn:nbn:de:0030-drops-43829},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.313},
  annote =	{Keywords: Concurrency, Automata, Higher-Order, Verification, Model-Checking}
}
Document
Parameterised Pushdown Systems with Non-Atomic Writes

Authors: Matthew Hague

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)


Abstract
We consider the master/slave parameterised reachability problem for networks of pushdown systems, where communication is via a global store using only non-atomic reads and writes. We show that the control-state reachability problem is decidable. As part of the result, we provide a constructive extension of a theorem by Ehrenfeucht and Rozenberg to produce an NFA equivalent to certain kinds of CFG. Finally, we show that the non-parameterised version is undecidable.

Cite as

Matthew Hague. Parameterised Pushdown Systems with Non-Atomic Writes. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 457-468, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)


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@InProceedings{hague:LIPIcs.FSTTCS.2011.457,
  author =	{Hague, Matthew},
  title =	{{Parameterised Pushdown Systems with Non-Atomic Writes}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{457--468},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.457},
  URN =		{urn:nbn:de:0030-drops-33485},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.457},
  annote =	{Keywords: Verification, Concurrency, Pushdown Systems, Reachability, Parameterised Systems, Non-atomicity}
}
Document
The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems

Authors: Matthew Hague and Anthony Widjaja To

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)


Abstract
We study (collapsible) higher-order pushdown systems --- theoretically robust and well-studied models of higher-order programs --- along with their natural subclass called (collapsible) higher-order basic process algebras. We provide a comprehensive analysis of the model checking complexity of a range of both branching-time and linear-time temporal logics. We obtain tight bounds on data, expression, and combined-complexity for both (collapsible) higher-order pushdown systems and (collapsible) higher-order basic process algebra. At order-$k$, results range from polynomial to $(k+1)$-exponential time. Finally, we study (collapsible) higher-order basic process algebras as graph generators and show that they are almost as powerful as (collapsible) higher-order pushdown systems up to MSO interpretations.

Cite as

Matthew Hague and Anthony Widjaja To. The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 228-239, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{hague_et_al:LIPIcs.FSTTCS.2010.228,
  author =	{Hague, Matthew and To, Anthony Widjaja},
  title =	{{The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{228--239},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.228},
  URN =		{urn:nbn:de:0030-drops-28663},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.228},
  annote =	{Keywords: Higher-Order, Collapsible, Pushdown Systems, Temporal Logics, Complexity, Model Checking}
}
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