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**Published in:** LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their transductions. The satisfiability problem is known to be undecidable even without rational transductions. It is known to be NExptime-complete without transductions, if the subword relations between variables do not have a cyclic dependency between them. We show that the satisfiability problem stays decidable in this fragment even when rational transductions are added. It is 2NExptime-complete with context-free membership, and NExptime-complete with only regular membership. For the lower bound we prove a technical lemma that is of independent interest: The length of the shortest word in the intersection of a pushdown automaton (of size 𝒪(n)) and n finite-state automata (each of size 𝒪(n)) can be double exponential in n.

C. Aiswarya, Soumodev Mal, and Prakash Saivasan. Satisfiability of Context-Free String Constraints with Subword-Ordering and Transducers. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aiswarya_et_al:LIPIcs.STACS.2024.5, author = {Aiswarya, C. and Mal, Soumodev and Saivasan, Prakash}, title = {{Satisfiability of Context-Free String Constraints with Subword-Ordering and Transducers}}, booktitle = {41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)}, pages = {5:1--5:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-311-9}, ISSN = {1868-8969}, year = {2024}, volume = {289}, editor = {Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.5}, URN = {urn:nbn:de:0030-drops-197154}, doi = {10.4230/LIPIcs.STACS.2024.5}, annote = {Keywords: satisfiability, subword, string constraints, context-free, transducers} }

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**Published in:** LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

We introduce weighted one-deterministic-counter automata (odca). These are weighted one-counter automata (oca) with the property of counter-determinacy, meaning that all paths labelled by a given word starting from the initial configuration have the same counter-effect. Weighted odcas are a strict extension of weighted visibly ocas, which are weighted ocas where the input alphabet determines the actions on the counter.
We present a novel problem called the co-VS (complement to a vector space) reachability problem for weighted odcas over fields, which seeks to determine if there exists a run from a given configuration of a weighted odca to another configuration whose weight vector lies outside a given vector space. We establish two significant properties of witnesses for co-VS reachability: they satisfy a pseudo-pumping lemma, and the lexicographically minimal witness has a special form. It follows that the co-VS reachability problem is in 𝖯.
These reachability problems help us to show that the equivalence problem of weighted odcas over fields is in 𝖯 by adapting the equivalence proof of deterministic real-time ocas [Stanislav Böhm and Stefan Göller, 2011] by Böhm et al. This is a step towards resolving the open question of the equivalence problem of weighted ocas. Finally, we demonstrate that the regularity problem, the problem of checking whether an input weighted odca over a field is equivalent to some weighted automaton, is in 𝖯. We also consider boolean odcas and show that the equivalence problem for (non-deterministic) boolean odcas is in PSPACE, whereas it is undecidable for (non-deterministic) boolean ocas.

Prince Mathew, Vincent Penelle, Prakash Saivasan, and A.V. Sreejith. Weighted One-Deterministic-Counter Automata. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mathew_et_al:LIPIcs.FSTTCS.2023.39, author = {Mathew, Prince and Penelle, Vincent and Saivasan, Prakash and Sreejith, A.V.}, title = {{Weighted One-Deterministic-Counter Automata}}, booktitle = {43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)}, pages = {39:1--39:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-304-1}, ISSN = {1868-8969}, year = {2023}, volume = {284}, editor = {Bouyer, Patricia and Srinivasan, Srikanth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.39}, URN = {urn:nbn:de:0030-drops-194129}, doi = {10.4230/LIPIcs.FSTTCS.2023.39}, annote = {Keywords: One-counter automata, Equivalence, Weighted automata, Reachability} }

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**Published in:** LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

We present a framework that provides deterministic consistency algorithms for given memory models. Such an algorithm checks whether the executions of a shared-memory concurrent program are consistent under the axioms defined by a model. For memory models like SC and TSO, checking consistency is NP-complete. Our framework shows, that despite the hardness, fast deterministic consistency algorithms can be obtained by employing tools from fine-grained complexity.
The framework is based on a universal consistency problem which can be instantiated by different memory models. We construct an algorithm for the problem running in time 𝒪^*(2^k), where k is the number of write accesses in the execution that is checked for consistency. Each instance of the framework then admits an 𝒪^*(2^k)-time consistency algorithm. By applying the framework, we obtain corresponding consistency algorithms for SC, TSO, PSO, and RMO. Moreover, we show that the obtained algorithms for SC, TSO, and PSO are optimal in the fine-grained sense: there is no consistency algorithm for these running in time 2^{o(k)} unless the exponential time hypothesis fails.

Peter Chini and Prakash Saivasan. A Framework for Consistency Algorithms. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chini_et_al:LIPIcs.FSTTCS.2020.42, author = {Chini, Peter and Saivasan, Prakash}, title = {{A Framework for Consistency Algorithms}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {42:1--42:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.42}, URN = {urn:nbn:de:0030-drops-132833}, doi = {10.4230/LIPIcs.FSTTCS.2020.42}, annote = {Keywords: Consistency, Weak Memory, Fine-Grained Complexity} }

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**Published in:** LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

We investigate the fine-grained complexity of liveness verification for leader contributor systems. These consist of a designated leader thread and an arbitrary number of identical contributor threads communicating via a shared memory. The liveness verification problem asks whether there is an infinite computation of the system in which the leader reaches a final state infinitely often. Like its reachability counterpart, the problem is known to be NP-complete. Our results show that, even from a fine-grained point of view, the complexities differ only by a polynomial factor.
Liveness verification decomposes into reachability and cycle detection. We present a fixed point iteration solving the latter in polynomial time. For reachability, we reconsider the two standard parameterizations. When parameterized by the number of states of the leader L and the size of the data domain D, we show an (L + D)^O(L + D)-time algorithm. It improves on a previous algorithm, thereby settling an open problem. When parameterized by the number of states of the contributor C, we reuse an O^*(2^C)-time algorithm. We show how to connect both algorithms with the cycle detection to obtain algorithms for liveness verification. The running times of the composed algorithms match those of reachability, proving that the fine-grained lower bounds for liveness verification are met.

Peter Chini, Roland Meyer, and Prakash Saivasan. Complexity of Liveness in Parameterized Systems. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chini_et_al:LIPIcs.FSTTCS.2019.37, author = {Chini, Peter and Meyer, Roland and Saivasan, Prakash}, title = {{Complexity of Liveness in Parameterized Systems}}, booktitle = {39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)}, pages = {37:1--37:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-131-3}, ISSN = {1868-8969}, year = {2019}, volume = {150}, editor = {Chattopadhyay, Arkadev and Gastin, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.37}, URN = {urn:nbn:de:0030-drops-115993}, doi = {10.4230/LIPIcs.FSTTCS.2019.37}, annote = {Keywords: Liveness Verification, Fine-Grained Complexity, Parameterized Systems} }

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**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

We address the problem of specifying and verifying quantitative properties of procedural programs. These properties typically involve constraints on the relative cumulated costs of executing various tasks (by invoking for instance some particular procedures) within the scope of the execution of some particular procedure. An example of such properties is "within the execution of each invocation of procedure P, the time spent in executing invocations of procedure Q is less than 20 % of the total execution time". We introduce specification formalisms, both automata-based and logic-based, for expressing such properties, and we study the links between these formalisms and their application in model-checking. On one side, we define Constrained Pushdown Systems (CPDS), an extension of pushdown systems with constraints, expressed in Presburger arithmetics, on the numbers of occurrences of each symbol in the alphabet within invocation intervals (subcomputations between matching pushes and pops), and on the other side, we introduce a higher level specification language that is a quantitative extension of CaRet (the Call-Return temporal logic) called QCaRet where nested quantitative constraints over procedure invocation intervals are expressible using Presburger arithmetics. Then, we investigate (1) the decidability of the reachability and repeated reachability problems for CPDS, and (2) the effective reduction of the model-checking problem of procedural programs (modeled as visibly pushdown systems) against QCaRet formulas to these problems on CPDS.

Mohamed Faouzi Atig, Ahmed Bouajjani, K. Narayan Kumar, and Prakash Saivasan. Verifying Quantitative Temporal Properties of Procedural Programs. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{atig_et_al:LIPIcs.CONCUR.2018.15, author = {Atig, Mohamed Faouzi and Bouajjani, Ahmed and Narayan Kumar, K. and Saivasan, Prakash}, title = {{Verifying Quantitative Temporal Properties of Procedural Programs}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {15:1--15:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.15}, URN = {urn:nbn:de:0030-drops-95531}, doi = {10.4230/LIPIcs.CONCUR.2018.15}, annote = {Keywords: Verification, Formal Methods, Pushdown systems, Visibly pushdown, Quantitative Temporal Properties} }

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**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

We investigate the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that, under very mild assumptions, every two disjoint WSTS languages are regular separable: There is a regular language containing one of them and being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. In particular, no subclass of WSTS languages beyond the regular languages is closed under complement. Our second result shows that for Petri nets, the complexity of the backwards coverability algorithm yields a bound on the size of the regular separator. We complement it by a lower bound construction.

Wojciech Czerwinski, Slawomir Lasota, Roland Meyer, Sebastian Muskalla, K. Narayan Kumar, and Prakash Saivasan. Regular Separability of Well-Structured Transition Systems. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2018.35, author = {Czerwinski, Wojciech and Lasota, Slawomir and Meyer, Roland and Muskalla, Sebastian and Narayan Kumar, K. and Saivasan, Prakash}, title = {{Regular Separability of Well-Structured Transition Systems}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {35:1--35:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.35}, URN = {urn:nbn:de:0030-drops-95733}, doi = {10.4230/LIPIcs.CONCUR.2018.35}, annote = {Keywords: regular separability, wsts, coverability languages, Petri nets} }

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**Published in:** LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

In this paper, we consider asynchronous programs consisting of multiple recursive threads running in parallel. Each of the threads is equipped with a multi-set. The threads can create tasks and post them onto the multi-sets or read a task from their own. In addition, they can synchronise through a finite set of locks. In this paper, we show that the reachability problem for such class of asynchronous programs is undecidable even under the nested locking policy. We then show that the reachability problem becomes decidable (Exp-space-complete) when the locks are not allowed to be held across tasks. Finally, we show that the problem is NP-complete when in addition to previous restrictions, threads always read tasks from the same state.

Mohamed Faouzi Atig, Ahmed Bouajjani, K. Narayan Kumar, and Prakash Saivasan. Verification of Asynchronous Programs with Nested Locks. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{atig_et_al:LIPIcs.FSTTCS.2017.11, author = {Atig, Mohamed Faouzi and Bouajjani, Ahmed and Narayan Kumar, K. and Saivasan, Prakash}, title = {{Verification of Asynchronous Programs with Nested Locks}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {11:1--11:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-055-2}, ISSN = {1868-8969}, year = {2018}, volume = {93}, editor = {Lokam, Satya and Ramanujam, R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.11}, URN = {urn:nbn:de:0030-drops-84106}, doi = {10.4230/LIPIcs.FSTTCS.2017.11}, annote = {Keywords: asynchronous programs locks concurrency multi-set pushdown systems, multi-threaded programs, reachability, model checking, verification, nested lockin} }

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

We study the size and the complexity of computing finite state automata (FSA) representing and approximating the downward and the upward closure of Petri net languages with coverability as the acceptance condition.
We show how to construct an FSA recognizing the upward closure of a Petri net language in doubly-exponential time, and therefore the size is at most doubly exponential.
For downward closures, we prove that the size of the minimal automata can be non-primitive recursive.
In the case of BPP nets, a well-known subclass of Petri nets, we show that an FSA accepting the downward/upward closure can be constructed in exponential time.
Furthermore, we consider the problem of checking whether a simple regular language is included in the downward/upward closure of a Petri net/BPP net language.
We show that this problem is EXPSPACE-complete (resp. NP-complete) in the case of Petri nets (resp. BPP nets).
Finally, we show that it is decidable whether a Petri net language is upward/downward closed.

Mohamed Faouzi Atig, Roland Meyer, Sebastian Muskalla, and Prakash Saivasan. On the Upward/Downward Closures of Petri Nets. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{atig_et_al:LIPIcs.MFCS.2017.49, author = {Atig, Mohamed Faouzi and Meyer, Roland and Muskalla, Sebastian and Saivasan, Prakash}, title = {{On the Upward/Downward Closures of Petri Nets}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {49:1--49:14}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.49}, URN = {urn:nbn:de:0030-drops-81278}, doi = {10.4230/LIPIcs.MFCS.2017.49}, annote = {Keywords: Petri nets, BPP nets, downward closure, upward closure} }

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**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Bounded context switching (BCS) is an under-approximate method for finding violations to safety properties in shared-memory concurrent programs. Technically, BCS is a reachability problem that is known to be NP-complete. Our contribution is a parameterized analysis of BCS.
The first result is an algorithm that solves BCS when parameterized by the number of context switches (cs) and the size of the memory (m) in O*(m^(cs)2^(cs)). This is achieved by creating instances of the easier problem Shuff which we solve via fast subset convolution. We also present a lower bound for BCS of the form m^o(cs / log(cs)), based on the exponential time hypothesis. Interestingly, the gap is closely related to a conjecture that has been open since FOCS'07. Further, we prove that BCS admits no polynomial kernel.
Next, we introduce a measure, called scheduling dimension, that captures the complexity of schedules. We study BCS parameterized by the scheduling dimension (sdim) and show that it can be solved in O*((2m)^(4sdim)4^t), where t is the number of threads. We consider variants of the problem for which we obtain (matching) upper and lower bounds.

Peter Chini, Jonathan Kolberg, Andreas Krebs, Roland Meyer, and Prakash Saivasan. On the Complexity of Bounded Context Switching. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chini_et_al:LIPIcs.ESA.2017.27, author = {Chini, Peter and Kolberg, Jonathan and Krebs, Andreas and Meyer, Roland and Saivasan, Prakash}, title = {{On the Complexity of Bounded Context Switching}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {27:1--27:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.27}, URN = {urn:nbn:de:0030-drops-78730}, doi = {10.4230/LIPIcs.ESA.2017.27}, annote = {Keywords: Shared memory concurrency, safety verification, fixed-parameter tractability, exponential time hypothesis, bounded context switching} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

This paper addresses the reachability problem for pushdown systems communicating via shared memory. It is already known that this problem is undecidable. It turns out that undecidability holds even if the shared memory consists of a single boolean variable. We propose a restriction on the behaviours of such systems, called stage bound, towards decidability. A k stage bounded run can be split into a k stages, such that in each stage there is at most one process writing to the shared memory while any number of processes may read from it. We consider several versions of stage-bounded systems and establish decidability and complexity results.

Mohamed Faouzi Atig, Ahmed Bouajjani, K. Narayan Kumar, and Prakash Saivasan. On Bounded Reachability Analysis of Shared Memory Systems. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 611-623, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{atig_et_al:LIPIcs.FSTTCS.2014.611, author = {Atig, Mohamed Faouzi and Bouajjani, Ahmed and Narayan Kumar, K. and Saivasan, Prakash}, title = {{On Bounded Reachability Analysis of Shared Memory Systems}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {611--623}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.611}, URN = {urn:nbn:de:0030-drops-48754}, doi = {10.4230/LIPIcs.FSTTCS.2014.611}, annote = {Keywords: Reachability problem, Pushdown systems, Counter systems} }

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