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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.  ...  Preservation of recognisability results for prefix-rewrite systems on words were known since Büchi [11] (cf. also [3, 12] and the book by Book & Otto [4] ).  ... 
arXiv:1410.4065v1 fatcat:ch6ld55th5fpxhixr54s776dta

Recursion Schemes, Collapsible Pushdown Automata and Higher-Order Model Checking [chapter]

Luke Ong
2013 Lecture Notes in Computer Science  
Collapsible pushdown automata are a generalisation of pushdown automata to higher-order stacks -which are iterations of stack of stacks -that contain symbols equipped with links.  ...  We study and compare the expressive power of the two models and the algorithmic properties of infinite structures such as trees and graphs generated by them.  ...  I am grateful to all my collaborators for their help. Thanks are also due to EPSRC for financial support.  ... 
doi:10.1007/978-3-642-37064-9_3 fatcat:vmzogjyskfahbeklhyssyajvuy

Higher-Order Model Checking: An Overview

Luke Ong
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Advances have been made in determining the expressive power of recursion schemes and other higher-order families of generators, automata-theoretic characterisations of these generator families, and the  ...  Because the trees generated by recursion schemes are computation trees of higher-order functional programs, higherorder model checking provides a foundation for model checkers of such programming languages  ...  Acknowledgements: The author is grateful to Takeshi Tsukada for helpful comments on the paper.  ... 
doi:10.1109/lics.2015.9 dblp:conf/lics/Ong15 fatcat:55bfxqlkuzhbtgmzc32m46ooku

Collapsible Pushdown Automata and Recursion Schemes

M. Hague, A.S. Murawski, C.-H.L. Ong, O. Serre
2008 Logic in Computer Science  
Collapsible pushdown automata (CPDA) are a new kind of higher-order pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it.  ...  In addition to the higher-order stack operations push i and pop i , CPDA have an important operation called collapse, whose effect is to "collapse" a stack s to the prefix as indicated by the link from  ...  Introduction Higher-order pushdown automata (PDA) were first introduced by Maslov [18] as accepting devices for word languages.  ... 
doi:10.1109/lics.2008.34 dblp:conf/lics/HagueMOS08 fatcat:42iwbcfoebc33gjlfvzazv2gte

Collapsible Pushdown Automata and Recursion Schemes

Matthew Hague, Andrzej S. Murawski, C.-H. Luke Ong, Olivier Serre
2017 ACM Transactions on Computational Logic  
Collapsible pushdown automata (CPDA) are a new kind of higher-order pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it.  ...  In addition to the higher-order stack operations push i and pop i , CPDA have an important operation called collapse, whose effect is to "collapse" a stack s to the prefix as indicated by the link from  ...  Introduction Higher-order pushdown automata (PDA) were first introduced by Maslov [18] as accepting devices for word languages.  ... 
doi:10.1145/3091122 fatcat:keajcf7tvvbe3euz4zfc7mtkaa

The Different Shades of Infinite Session Types [article]

Simon J. Gay and Diogo Poças and Vasco T. Vasconcelos
2022 arXiv   pre-print
of automata: finite-state, 1-counter, pushdown and 2-counter.  ...  We also consider previous work on context-free session types (and extend it to higher-order) and nested session types, and locate them on our spectrum of infinite types.  ...  This largest prefix exists since L is prefix-closed and non-empty (in particular, the empty word must belong to L).  ... 
arXiv:2201.08275v1 fatcat:di3xp4jiuvfbbba3vtfpydqv44

First-Order Model Checking on Generalisations of Pushdown Graphs [article]

Alexander Kartzow
2012 arXiv   pre-print
Our decidability result for collapsible pushdown graph relies on the fact that level 2 collapsible pushdown graphs are uniform tree-automatic.  ...  Moreover, nested pushdown trees are first-order interpretable in collapsible pushdown graphs of level 2.  ...  Automata that may be used for this approach are, e.g., Turing machines, finite automata, pushdown systems or collapsible pushdown systems.  ... 
arXiv:1202.0137v1 fatcat:eosire2rwzan3h7hszsnijfwfy

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
Both process algebras (or term rewriting systems) and automata (or finite control machines) are being used as specification formalisms.  ...  Algorithmic methods can be based on fixpoint theory, automata theory or (constrained) logic programming.  ...  of pushdown automata, one-counter automata, and one-counter nets.  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

Saturation algorithms for model-checking pushdown systems

Arnaud Carayol, Matthew Hague
2014 Electronic Proceedings in Theoretical Computer Science  
We present a survey of the saturation method for model-checking pushdown systems.  ...  The formalism used by Büchi is not that of pushdown automata but that of prefix word-rewriting systems (which he calls regular canonical systems).  ...  Recently, these systems were generalised to collapsible pushdown systems (via panic automata [31] ), providing an automata model without the need for the safety constraint [25] .  ... 
doi:10.4204/eptcs.151.1 fatcat:546kymvwxnfgxikrpfr2ozl5ry

Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties [article]

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 arXiv   pre-print
This is obtained thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible  ...  pushdown automata.  ...  Order-recursion schemes and order-collapsible pushdown automata are equi-expressive for generating trees.  ... 
arXiv:2010.06366v2 fatcat:htqiqtp3rfaxxattbycq4hlhsq

Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 ACM Transactions on Computational Logic  
This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible  ...  pushdown automata.  ...  Order-recursion schemes and order-collapsible pushdown automata are equi-expressive for generating trees.  ... 
doi:10.1145/3452917 fatcat:e7pseftknfcxzdwunjwrk6ofkm

Ordered Tree-Pushdown Systems

Lorenzo Clemente, Pawel Parys, Sylvain Salvati, Igor Walukiewicz, Marc Herbstritt
2015 Foundations of Software Technology and Theoretical Computer Science  
We define a new class of pushdown systems where the pushdown is a tree instead of a word.  ...  machine, and ordered annotated multipushdown systems.  ...  We kindly acknowledge stimulating discussions with Irène Durand, Géraud Sénizergues, and Jean-Marc Talbot.  ... 
doi:10.4230/lipics.fsttcs.2015.163 dblp:conf/fsttcs/ClementePSW15 fatcat:nk3iigwctzbyfasttkojjjhxoa

Winning Regions of Higher-Order Pushdown Games

Arnaud Carayol, Matthew Hague, Antoine Meyer, C.-H. Luke Ong, Olivier Serre
2008 Logic in Computer Science  
These automata generalise pushdown automata by the use of higher-order stacks, which are nested "stack of stacks" structures.  ...  In this paper we consider parity games defined by higher-order pushdown automata.  ...  Introduction Higher-order pushdown automata were introduced by Maslov [31] as a generalisation of pushdown automata and nested pushdown automata to extend the indexed languages introduced by Aho [1]  ... 
doi:10.1109/lics.2008.41 dblp:conf/lics/CarayolHMOS08 fatcat:lgkwjeewtzgvfcfpqan5dyckji

Ties between Parametrically Polymorphic Type Systems and Finite Control Automata [article]

Joseph Gil, Ori Roth
2020 arXiv   pre-print
We present a correspondence and bisimulation between variants of parametrically polymorphic type systems and variants of finite control automata, such as FSA, PDA, tree automata and Turing machine.  ...  correspondence we show that two recent celebrated results on automatic generation of fluent API are optimal in certain senses, present new results on the studied type systems, formulate open problems, and  ...  Rewrites of a pushdown. Rewrites of a pushdown auxiliary storage are the usual push and pop operations; we will see that these can be regarded as tree rewrites. Trees.  ... 
arXiv:2009.04437v3 fatcat:543tqv4aunbnlctk6mjh2c65ga

On Boundedness Problems for Pushdown Vector Addition Systems [article]

Jérôme Leroux, Grégoire Sutre, Patrick Totzke
2015 arXiv   pre-print
We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems.  ...  We show decidability in exponential time for one-dimensional systems.  ...  Praveen for insightful discussions. We also thank the anonymous referees for their useful comments and suggestions.  ... 
arXiv:1507.07362v1 fatcat:sgonsnc7mjcghey4er6vonl6oe
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