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On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems

Vincent Penelle, Sylvain Salvati, Grégoire Sutre, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets.  ...  The starting point of the present work was thus the conjecture that Karp and Miller's algorithm would be a decision tool for termination and boundedness for higher-order pushdown VASS (or HOPVASS for short  ...  Higher-order pushdown vector addition systems with states. We let N denote the set of natural numbers N = {0, 1, . . .} and we let Z denote the set of integers Z = {. . . , −1, 0, 1, . . .}.  ... 
doi:10.4230/lipics.fsttcs.2018.44 dblp:conf/fsttcs/PenelleSS18 fatcat:pmpp2zxolrdxldsjwoev7tt4pa

On Boundedness Problems for Pushdown Vector Addition Systems [chapter]

Jérôme Leroux, Grégoire Sutre, Patrick Totzke
2015 Lecture Notes in Computer Science  
Counter boundedness seems to be the more intricate problem. We show decidability in exponential time for one-dimensional systems.  ...  We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems.  ...  Acknowledgments The authors wish to thank M. Praveen for insightful discussions. We also thank the anonymous referees for their useful comments and suggestions.  ... 
doi:10.1007/978-3-319-24537-9_10 fatcat:7yfqimz4hjhovfrpowwlhlvhlq

On Boundedness Problems for Pushdown Vector Addition Systems [article]

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

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

Morten Kühnrich, Stefan Schwoon, Jiří Srba, Stefan Kiefer
2009 Lecture Notes in Computer Science  
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  ...  The main novelty of our work is that we deal with semirings without the boundedness restriction. Our study is motivated by several applications from interprocedural dataflow analysis.  ...  It moreover preserves inequality because the addition does so, and ⊑ is a total order.  ... 
doi:10.1007/978-3-642-00596-1_31 fatcat:rsgdshr45faxdks34la7rfkk2i

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  ...  The main novelty of our work is that we deal with semirings without the boundedness restriction. Our study is motivated by several applications from interprocedural dataflow analysis.  ...  It moreover preserves inequality because the addition does so, and ⊑ is a total order.  ... 
arXiv:0901.0501v2 fatcat:vtk63shp3fc6tbiejtk3i2demy

Scope-Bounded Reachability in Valence Systems [article]

Aneesh K. Shetty and S. Krishna and Georg Zetzsche
2021 arXiv   pre-print
This framework captures pushdowns, vector addition systems, integer vector addition systems, and combinations thereof.  ...  Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem.  ...  On the coverability problem for pushdown vector addition systems in one dimension. In Proceedings of ICALP 2015, volume 9135 of Lecture Notes in Computer Science, pages 324-336.  ... 
arXiv:2108.00963v1 fatcat:rxuuxuq4hrfvta6vmi32tbbami

Regular Separability and Intersection Emptiness Are Independent Problems

Ramanathan S. Thinniyam, Georg Zetzsche, Michael Wagner
2019 Foundations of Software Technology and Theoretical Computer Science  
On the positive side, it was shown that regular separability is decidable for several subclasses of vector addition systems (VASS): for one-dimensional VASS [29] , for commutative VASS languages [9] ,  ...  This was recently strengthened to undecidability already for visibly pushdown languages [28] and one-counter languages [29] .  ...  The definition of C is based on reset vector addition systems. Reset Vector Addition Systems.  ... 
doi:10.4230/lipics.fsttcs.2019.51 dblp:conf/fsttcs/ThinniyamZ19 fatcat:rklvkbma6jcexd55xddgo4glsu

General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and Beyond [chapter]

Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche
2021 Lecture Notes in Computer Science  
problem on languages.  ...  As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs—such as OCaml programs using Lwt—and undecidability of liveness verification  ...  The diagonal problem was then shown to be decidable for higher-order pushdown automata [15] and then for word schemes [7] .  ... 
doi:10.1007/978-3-030-72016-2_24 fatcat:isvi7y2cgnc5bjaxzkey77eshm

A Counting Logic for Structure Transition Systems

Lukasz Kaiser, Simon Leßenich, Marc Herbstritt
2012 Annual Conference for Computer Science Logic  
We propose a counting logic Qµ[#MSO] which allows to express questions like the ones above, and also many boundedness problems studied so far.  ...  These properties are used to prove decidability of Qµ[#MSO] on tree-producing pushdown systems, a generalization of both pushdown systems and regular tree grammars.  ...  We are very grateful to Igor Walukiewicz for pointing out that the methods from [19] can also be applied in the quantitative setting, as is done in Section 5.  ... 
doi:10.4230/lipics.csl.2012.366 dblp:conf/csl/KaiserL12 fatcat:o66rmshj3bf3bhgsyb5nkjb6lm

General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and Beyond [article]

Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche
2022 arXiv   pre-print
problem on languages.  ...  As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs -- such as OCaml programs using Lwt -- and undecidability of liveness  ...  The diagonal problem was then shown to be decidable for higher-order pushdown automata [HKO16] and then for word schemes [CPSW16] .  ... 
arXiv:2101.08611v3 fatcat:sdvr72kwyjctjo7cf2qkuidjvy

What Makes Petri Nets Harder to Verify: Stack or Data? [chapter]

Ranko Lazić, Patrick Totzke
2016 Lecture Notes in Computer Science  
classes of systems based on Petri nets: Ackermann-hardness for unordered data Petri nets, and Tower-hardness for pushdown vector addition systems.  ...  We show how the yardstick construction of Stockmeyer, also developed as counter bootstrapping by Lipton, can be adapted and extended to obtain new lower bounds for the coverability problem for two prominent  ...  Pushdown Vector Addition Systems.  ... 
doi:10.1007/978-3-319-51046-0_8 fatcat:lee6i2fc6rbehpurbtkrhuvxqi

Unboundedness Problems for Languages of Vector Addition Systems

Wojciech Czerwinski, Piotr Hofman, Georg Zetzsche, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language.  ...  In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision procedures for such languages.  ...  Acknowledgements We are indebted to Mohamed Faouzi Atig for suggesting to study separability by bounded languages, which was the starting point for this work.  ... 
doi:10.4230/lipics.icalp.2018.119 dblp:conf/icalp/CzerwinskiHZ18 fatcat:uq7l2bzg3jdmjokhi2n5rtybsq

Modeling and Verification of Infinite Systems with Resources

Martin Lang, Christof Löding, Thomas Schwentick
2013 Logical Methods in Computer Science  
In these systems, we investigate bounds on the resource consumption for reachability questions.  ...  Subsequently, we use this framework to solve the bounded reachability problem for resource prefix replacement systems.  ...  Additionally, there is currently some effort to extend this line of research to the area of pushdown systems.  ... 
doi:10.2168/lmcs-9(4:22)2013 fatcat:3ysai7on65dwhpo7kkquq6bppa

Parity Games Played on Transition Graphs of One-Counter Processes [chapter]

Olivier Serre
2006 Lecture Notes in Computer Science  
For parity games on pushdown graphs, it is known from [22] that deciding the winner is an ExpTime-complete problem.  ...  An important corollary of this result is that the µ-calculus model checking problem for pushdown processes is Exp-Time-complete.  ...  I would like to acknowledge the anonymous referees for their helpful suggestions and remarks.  ... 
doi:10.1007/11690634_23 fatcat:tsip6s4xqfcevo3bt7x5joe2cq

Unboundedness problems for languages of vector addition systems [article]

Wojciech Czerwiński and Piotr Hofman and Georg Zetzsche
2018 arXiv   pre-print
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language.  ...  In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision procedures for such languages.  ...  Acknowledgements We are indebted to Mohamed Faouzi Atig for suggesting to study separability by bounded languages, which was the starting point for this work.  ... 
arXiv:1802.06683v1 fatcat:bqxmgoeeyfhr5mxrrojnebiqui
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