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Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One *

Diego Figueira, Ranko Lazić, Jérôme Leroux, Filip Mazowiecki, Grégoire Sutre, R Lazic@warwick, Uk
unpublished
The one-dimensional case is a generalisation of the extensively studied one-counter nets, and it was recently established polynomial-time complete provided counter updates are given in unary.  ...  Our main contribution is to determine the complexity when the encoding is binary: polynomial-space complete. 1 Introduction Background.  ...  To verify if a configuration c with a value bounded by 2 |B| is reachable, we guess a complete run for c in nondeterministic polynomial space.  ... 
fatcat:4era4n3pxvgvzesayr2o3xwczu

Context-Bounded Verification of Thread Pools [article]

Pascal Baumann, Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche
2021 arXiv   pre-print
In particular, we show a polynomial-time construction of downward closures of languages accepted by succinct pushdown automata as doubly succinct nondeterministic finite automata.  ...  We show that the safety verification problem for thread-pooled, context-bounded, Boolean programs is EXPSPACE-complete, even if the size of the thread pool and the context bound are given in binary.  ...  ACKNOWLEDGMENTS This research was sponsored in part by the Deutsche Forschungsgemeinschaft project 389792660 TRR 248-CPEC and by the European Research Council under the Grant Agreement 610150 (http://www.impact-erc.eu  ... 
arXiv:2111.09022v1 fatcat:yygoghmwozarxm6ol2vjg5prte

Presburger arithmetic with stars, rational subsets of graph groups, and nested zero tests

Christoph Haase, Georg Zetzsche
2019 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
In particular, this enables us to obtain a complete description of the complexity landscape of the rational subset membership problem for fixed graph groups: If the graph is a clique, the problem is NL-complete  ...  We prove that the satisfiability problem for existential Presburger arithmetic with stars is NEXP-complete and that all three problems are polynomially inter-reducible.  ...  We are indebted to Markus Lohrey for fruitful discussions about graph groups, some of which provided key insights that found their way into the present paper.  ... 
doi:10.1109/lics.2019.8785850 dblp:conf/lics/HaaseZ19 fatcat:luvx6cwuzbfnvp2kfmd7peo7ua

Reachability in Two-Dimensional Vector Addition Systems with States: One Test is for Free [article]

Jérôme Leroux, Grégoire Sutre
2020 arXiv   pre-print
We show that reachability is still solvable in polynomial space for 2-TVASS.  ...  As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles.  ...  From that bound, we deduce that the reachability problem for 2-TVASS is decidable in polynomial space, and so is PSPACE-complete.  ... 
arXiv:2007.09096v1 fatcat:7n5u5yzc4vck3jkzkdqgblcfse

Reasoning about Data Repetitions with Counter Systems

Stephane Demri, Diego Figueira, M. Praveen
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system. Complete version of [DFP13] .  ...  This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts.  ...  There is a polynomial-space reduction from Reach(VASS) into SAT(PLRV).  ... 
doi:10.1109/lics.2013.8 dblp:conf/lics/DemriFP13 fatcat:bz4azd6m2nag5b2jgz4hfalu2e

Reasoning about data repetitions with counter systems

Stéphane Demri, Diego Figueira, M Praveen, Thomas Schwentick
2016 Logical Methods in Computer Science  
This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts.  ...  For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.  ...  There is a polynomial-space reduction from Reach(VASS) into SAT(PLRV).  ... 
doi:10.2168/lmcs-12(3:1)2016 fatcat:qz7esthlxzd3td2gicwt43d3oe

Modular Path Queries with Arithmetic [article]

Jakub Michaliszyn and Jan Otop and Piotr Wieczorek
2021 arXiv   pre-print
The resulting formalism is computationally attractive - queries can be answered in non-deterministic logarithmic space in the size of the database.  ...  To express complex properties in a modular way, we introduce labelling-generating ontologies.  ...  The Z-reachability problem for unary VASS of the fixed dimension (which is m in the reduction) is in NL [8, Therem 19] .  ... 
arXiv:2002.04460v5 fatcat:cy44rb2gcnhgll4h5tfi6lnzta

Subject index volumes 1–200

1999 Theoretical Computer Science  
, ,2511 -dimension, ,2694 -dimension, , 2783 complete, 180 complexity class, 308, 309, 377 polynomial space computable functions, 916 complete for -, 215 subclass of -, 235 1 PSPACE = NP.  ...  ratio, 347 I variants of h-models, 601 variations of KMR, 1641 varieties, 1430, 1575, 1797 VASS (vector addition system with states), 891 finite -, 891 VASS's of dimension two, 859 Vazirani and Valiant  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Parametrized Universality Problems for One-Counter Nets

Shaull Almagor, Udi Boker, Piotr Hofman, Patrick Totzke, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an  ...  We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.  ...  The bounded universality problem of unambiguous one-counter nets with unary-encoded transition weights is in NC 2 , and in NL if the alphabet has only one letter, and for binary-encoded transition weights  ... 
doi:10.4230/lipics.concur.2020.47 dblp:conf/concur/AlmagorBHT20 fatcat:rjdsexzp6bebzidv44kybcoala

Parametrized Universality Problems for One-Counter Nets [article]

Shaull Almagor, Udi Boker, Piotr Hofman, Patrick Totzke
2020 arXiv   pre-print
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an  ...  We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.  ...  Termination reduces to boundedness (finiteness of the reachability set) which is EXPSPACE-complete [22, 14] in general and PSPACE-complete for systems with fixed dimensions [23] .  ... 
arXiv:2005.03435v2 fatcat:iqkwxi44vfgzpnpzs4jidx7hii

Linear combinations of unordered data vectors

Piotr Hofman, Jerome Leroux, Patrick Totzke
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Based on a succinct representation of the involved permutations as integer linear constraints, we derive that positive instances can be witnessed in a bounded subset of the domain.  ...  We derive that in this case, expressibility is in NP, and in P for reversible instances.  ...  State equations are a fundamental invariant of the reachability relation for Petri nets and one of the important ingredients in the proof of decidability of the reachability problem [9] , [10] , [11  ... 
doi:10.1109/lics.2017.8005065 dblp:conf/lics/HofmanLT17 fatcat:iqckvt6gkbesvi3gtu3u3sgcpu

Subject Index to Volumes 1–75

2001 Information Processing Letters  
solvable, 1213, 2008 solvable in NC, 2299 O(n) time, 3828 polynomial time, 419, 478, 526, 884, 1771, 1891, 1912, 2154, 2518, 2572, 3063, 3460, 3796, 3977 solvable nondeterministically in polynomial  ...  Varma, 2525 Varol, Yaakov, 3700 VAS, 129, 307, 1392 languages, 3204 slices, 307 VASS, 1507 Vassiliev, V.A., 3535 Vassiliou, 744, 771 Vatan, Farrokh, 3373 VC dimension, 3333, 3403 VDL, 1059  ...  a matrix, 3196 order n matrices, 623 tensors, 719 the adjacency matrix of a line graph, 252 rank one matrices, 1164 matrix, 472 rank queries, 1761 r decision trees, 2406 rankable set, 3245 ranked, 1610  ... 
doi:10.1016/s0020-0190(01)00175-2 fatcat:5y67tfm6yfbblakrus5nnhs73e

Dagstuhl Reports, Volume 11, Issue 10, October 2021, Complete Issue [article]

2022
Dagstuhl Reports, Volume 11, Issue 10, October 2021, Complete Issue  ...  countably-dimensional Polish spaces.  ...  of parameters, defining the design space of a shape-optimisation problem, for tackling the challenges of the curse of dimensionality or decreasing the uncertainty in design's performance.  ... 
doi:10.4230/dagrep.11.10 fatcat:mqui2qttdrdt7p6y3nbkkodoci