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Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Matthew Hague, Luke Ong, Helmut Seidl
2008 Logical Methods in Computer Science  
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure.  ...  We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs.  ...  Acknowledgments We thank Olivier Serre and Arnaud Carayol for helpful discussions. We also thank the anonymous referees for their invaluable remarks.  ... 
doi:10.2168/lmcs-4(4:14)2008 fatcat:6bh45ha5mfg5zke6guh4mh7f4y

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems [chapter]

Matthew Hague, C. -H. Luke Ong
Foundations of Software Science and Computational Structures  
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure.  ...  We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs.  ...  Acknowledgments We thank Olivier Serre and Arnaud Carayol for helpful discussions. We also thank the anonymous referees for their invaluable remarks.  ... 
doi:10.1007/978-3-540-71389-0_16 dblp:conf/fossacs/HagueO07 fatcat:3sh675ig4fcynicwpxvtj2oiiu

Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting [article]

Lorenzo Clemente
2014 arXiv   pre-print
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees.  ...  This result subsumes and unifies similar analyses on collapsible and ordered pushdown systems.  ...  Reachability analysis of order-n collapsible/annotated pushdown systems is pn´1q-EXPTIME-complete, where ordinary pushdown systems correspond to the order-1 case.  ... 
arXiv:1410.4065v1 fatcat:ch6ld55th5fpxhixr54s776dta

Constrained Dynamic Tree Networks [chapter]

Matthew Hague, Vincent Penelle
2018 Lecture Notes in Computer Science  
We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model.  ...  We show that backwards reachability sets starting from regular sets of configurations are always regular. We provide an algorithm for computing backwards reachability sets using tree automata.  ...  Acknowledgments We thank the anonymous reviewers for their remarks. This work was supported by the Engineering and Physical Sciences Research Council [EP/K009907/1].  ... 
doi:10.1007/978-3-030-00250-3_4 fatcat:rwnnhcywlreb7ffocj6jjzbur4

Ordered Tree-Pushdown Systems

Lorenzo Clemente, Pawel Parys, Sylvain Salvati, Igor Walukiewicz, Marc Herbstritt
2015 Foundations of Software Technology and Theoretical Computer Science  
This follows from a preservation of recognizability result for the backward reachability relation of such systems.  ...  As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine  ...  for the analysis of pushdown systems, as well as the C-SHORe model-checker for annotated pushdown systems [?] . Contributions.  ... 
doi:10.4230/lipics.fsttcs.2015.163 dblp:conf/fsttcs/ClementePSW15 fatcat:nk3iigwctzbyfasttkojjjhxoa

Reachability in Higher-Order-Counters [chapter]

Alexander Heußner, Alexander Kartzow
2013 Lecture Notes in Computer Science  
Restricting HOCA (without 0-test) to level 2, we prove that global (forward or backward) reachability analysis is P-complete.  ...  graphs due to the pushdown graph's connection to the Caucal-hierarchy [6], and Hague and Ong determined the precise complexity of the global backwards reachability problem for HOPA: for level k it is  ...  The idea is to encode the pushdown symbol of level k, by the level 1 counter value modulo 3 (recall that P uses the pushdown alphabet {⊥, 0, 1}).  ... 
doi:10.1007/978-3-642-40313-2_47 fatcat:tyqmxynumjdc5fjbaqovqhvh4m

Reachability in Higher-Order-Counters [article]

Alexander Heußner, Alexander Kartzow
2013 arXiv   pre-print
Restricting (without 0-test) to level 2, we prove that global (forward or backward) reachability analysis is -complete.  ...  Higher-order counter automata () can be either seen as a restriction of higher-order pushdown automata () to a unary stack alphabet, or as an extension of counter automata to higher levels.  ...  The idea is to encode the pushdown symbol of level k, by the level 1 counter value modulo 3 (recall that P uses the pushdown alphabet {⊥, 0, 1}).  ... 
arXiv:1306.1069v1 fatcat:jcb2qzdiqbh6raniwlnfedppfy

C-SHORe

Christopher Broadbent, Arnaud Carayol, Matthew Hague, Olivier Serre
2013 Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13  
In particular it is able to use information gathered from an approximate forward reachability analysis to guide its backward search.  ...  Higher-order recursion schemes (HORS) have recently received much attention as a useful abstraction of higher-order functional programs with a number of new verification techniques employing HORS model-checking  ...  Acknowledgments We are extremely to Robin Neatherway and Naoki Kobayashi for help with benchmarking, Łukasz Kaiser for web-hosting, and for discussions with  ... 
doi:10.1145/2500365.2500589 dblp:conf/icfp/BroadbentCHS13 fatcat:dt2k4m7tungnhmvxfd2ydpkjma

Ordered Tree-Pushdown Systems [article]

Lorenzo Clemente, Paweł Parys, Sylvain Salvati, Igor Walukiewicz
2015 arXiv   pre-print
This follows from a preservation of recognizability result for the backward reachability relation of such systems.  ...  As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine  ...  We kindly acknowledge stimulating discussions with Irène Durand, Géraud Sénizergues, and Jean-Marc Talbot, and the anonymous reviewers for their helpful comments.  ... 
arXiv:1510.03278v1 fatcat:suhrbg4iyfho7ajpj4sqo4num4

Saturation of Concurrent Collapsible Pushdown Systems

Matthew Hague, Marc Herbstritt
2013 Foundations of Software Technology and Theoretical Computer Science  
Reachability problems for multi-stack collapsible pushdown systems have been little studied.  ...  To model higher-order procedures calls, a generalisation of pushdown stacks called collapsible pushdown stacks are required.  ...  We thus perform a backwards analysis for CPDS, resulting in a similar approach.  ... 
doi:10.4230/lipics.fsttcs.2013.313 dblp:conf/fsttcs/Hague13 fatcat:uft3k4zxpnftto2jc5yolpklgm

Pushdown flow analysis with abstract garbage collection

J. IAN JOHNSON, ILYA SERGEY, CHRISTOPHER EARL, MATTHEW MIGHT, DAVID VAN HORN
2014 Journal of functional programming  
Pushdown flow analysis grants unbounded yet computable polyvariance to the analysis of return-flow in higher-order programs.  ...  Conditional pushdown systems were developed for just such a conundrum, but existing methods are ill-suited for the dynamic nature of garbage collection.  ...  For completeness, we fully develop pushdown analysis for higher-order programs, including an efficient algorithm for computing reachable control states.  ... 
doi:10.1017/s0956796814000100 fatcat:wrkxdigcibdfdoy6i3axm6blhq

Symbolic Reachability Analysis of Higher-Order Context-Free Processes [chapter]

Ahmed Bouajjani, Antoine Meyer
2004 Lecture Notes in Computer Science  
We consider the problem of symbolic reachability analysis of higher-order context-free processes.  ...  We show that this result holds also in the case of backward reachability analysis under a regular constraint on configurations.  ...  Conclusion We have provided an automata-based symbolic technique for backward reachability analysis of higher-order context-free processes.  ... 
doi:10.1007/978-3-540-30538-5_12 fatcat:4c7qg7dkr5egfncxlv3w2wiawi

Pushdown Exception-Flow Analysis of Object-Oriented Programs [article]

Shuying Liang, Matthew Might, Thomas Gilray, David Van Horn
2013 arXiv   pre-print
Pushdown analysis of exceptions improves precision over the next best analysis, Bravenboer and Smaragdakis's Doop, by orders of magnitude.  ...  The recent development of pushdown control-flow analysis for the λ-calculus hints at a way to improve analysis of exceptions: a pushdown stack can precisely match catches to throws in the same way it matches  ...  This work directly draws on our previous work on pushdown analysis for higher-order programs [9] and introspective pushdown system (IPDS) for higherorder programs [10] .  ... 
arXiv:1302.2692v1 fatcat:fikdd6274bd67nfncjvkh6g7rm

Reachability analysis of first-order definable pushdown systems [article]

Lorenzo Clemente, Sławomir Lasota
2015 arXiv   pre-print
We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures.  ...  We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure.  ...  [9, 4] , annotated higher-order pushdown systems [25, 10] , and strongly normed multi-pushdown systems [14] .  ... 
arXiv:1504.02651v2 fatcat:sq2lqypu3rekhizrbsw223wop4

Interprocedural Dataflow Analysis over Weight Domains with Infinite Descending Chains [article]

Morten Kühnrich, Stefan Schwoon, Jiří Srba, Stefan Kiefer
2009 arXiv   pre-print
We demonstrate how the reachability problem for weighted pushdown automata can be reduced to solving equations in the framework mentioned above and we describe a few applications to demonstrate its usability  ...  Our study is motivated by several applications from interprocedural dataflow analysis.  ...  A similar conclusion about the complexity of the algorithm for computing successors can be drawn thanks to the (linear) connection between forward and backward reachability analysis described in Appendix  ... 
arXiv:0901.0501v2 fatcat:vtk63shp3fc6tbiejtk3i2demy
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