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Documents authored by Broadbent, Christopher H.

Found 2 Possible Name Variants:

Broadbent, Christopher H.

Document
DOI: 10.4230/LIPIcs.STACS.2012.589
The Limits of Decidability for First Order Logic on CPDA Graphs

Authors: Christopher H. Broadbent

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract
Higher-order pushdown automata (n-PDA) are abstract machines equipped with a nested 'stack of stacks of stacks'. Collapsible pushdown automata (n-CPDA) extend these devices by adding `links' to the stack and are equi-expressive for tree generation with simply typed lambda-Y terms. Whilst the configuration graphs of HOPDA are well understood, relatively little is known about the CPDA graphs. The order-2 CPDA graphs already have undecidable MSO theories but it was only recently shown by Kartzow [Kartzow 2010] that first-order logic is decidable at the second level. In this paper we show the surprising result that first-order logic ceases to be decidable at order-3 and above. We delimit the fragments of the decision problem to which our undecidability result applies in terms of quantifer alternation and the orders of CPDA links used. Additionally we exhibit a natural sub-hierarchy enjoying limited decidability.
Cite as

Christopher H. Broadbent. The Limits of Decidability for First Order Logic on CPDA Graphs. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 589-600, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{broadbent:LIPIcs.STACS.2012.589,
  author =	{Broadbent, Christopher H.},
  title =	{{The Limits of Decidability for First Order Logic on CPDA Graphs}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{589--600},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.589},
  URN =		{urn:nbn:de:0030-drops-34334},
  doi =		{10.4230/LIPIcs.STACS.2012.589},
  annote =	{Keywords: Collapsible Pushdown Automata, First Order Logic, Logical Reflection}
}

Broadbent, Christopher

Document
DOI: 10.4230/LIPIcs.CSL.2013.129
Saturation-Based Model Checking of Higher-Order Recursion Schemes

Authors: Christopher Broadbent and Naoki Kobayashi

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract
Model checking of higher-order recursion schemes (HORS) has recently been studied extensively and applied to higher-order program verification. Despite recent efforts, obtaining a scalable model checker for HORS remains a big challenge. We propose a new model checking algorithm for HORS, which combines two previous, independent approaches to higher-order model checking. Like previous type-based algorithms for HORS, it directly analyzes HORS and outputs intersection types as a certificate, but like Broadbent et al.'s saturation algorithm for collapsible pushdown systems (CPDS), it propagates information backward, in the sense that it starts with target configurations and iteratively computes their pre-images. We have implemented the new algorithm and confirmed that the prototype often outperforms TRECS and CSHORe, the state-of-the-art model checkers for HORS.
Cite as

Christopher Broadbent and Naoki Kobayashi. Saturation-Based Model Checking of Higher-Order Recursion Schemes. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 129-148, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{broadbent_et_al:LIPIcs.CSL.2013.129,
  author =	{Broadbent, Christopher and Kobayashi, Naoki},
  title =	{{Saturation-Based Model Checking of Higher-Order Recursion Schemes}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{129--148},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.129},
  URN =		{urn:nbn:de:0030-drops-41941},
  doi =		{10.4230/LIPIcs.CSL.2013.129},
  annote =	{Keywords: Model checking, higher-order recursion schemes, intersection types}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.160
On Bisimilarity of Higher-Order Pushdown Automata: Undecidability at Order Two

Authors: Christopher Broadbent and Stefan Göller

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
We show that bisimulation equivalence of order-two pushdown automata is undecidable. Moreover, we study the lower order problem of higher-order pushdown automata, which asks, given an order-k pushdown automaton and some k'<k, to determine if there exists a reachable configuration that is bisimilar to some order-k' pushdown automaton. We show that the lower order problem is undecidable for each k >= 2 even when the input k-PDA is deterministic and real-time.
Cite as

Christopher Broadbent and Stefan Göller. On Bisimilarity of Higher-Order Pushdown Automata: Undecidability at Order Two. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 160-172, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{broadbent_et_al:LIPIcs.FSTTCS.2012.160,
  author =	{Broadbent, Christopher and G\"{o}ller, Stefan},
  title =	{{On Bisimilarity of Higher-Order Pushdown Automata: Undecidability at Order Two}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{160--172},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.160},
  URN =		{urn:nbn:de:0030-drops-38583},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.160},
  annote =	{Keywords: Bisimulation equivalence, Higher-order pushdown automata}
}
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