arXiv subjects

Anton Wijs

Publications and source records attributed to Anton Wijs.

18 recordsLinked to original sources

arXiv2026

Evaluating Massively Parallel Algorithms for DFA Minimisation, Equivalence Checking and Inclusion Checking

We study parallel algorithms for the minimisation and equivalence checking of Deterministic Finite Automata (DFAs). Regarding DFA minimisation, we implement four different massively parallel algorithms on Graphics Processing Units~(GPUs). Our results confirm the expectations that the algorithm with the theoretically best time complexity is not practically suitable to run on GPUs due to the large amount of resources needed. We empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse. Furthermore, we introduce a novel algorithm based on partition refinement with an extra parallel partial transitive closure step and show that on specific benchmarks it has better run-time complexity and performs better in practice. In addition, we address checking the language equivalence and inclusion of two DFAs. We consider the Hopcroft-Karp algorithm, and explain how a variant of it can be parallelised for GPUs. We note that these problems can be encoded for the GPU-accelerated model checker \GPUexplore, allowing the use its lockless hash table and fine-grained parallel work distribution mechanism.

cs.FL↗

arXiv2026

Scalable Deductive Verification of Data-Level Parallel Programs

This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested) quantifiers, so suitable triggers can be generated for these expressions. We have proven this rewrite technique correct in a theorem prover. Second, we make reasoning about potentially overlapping arrays easier, by providing specification constructs to indicate and verify that two arrays are not aliases, or that they are immutable, so they can be modelled as mathematical sequences. All our techniques are implemented in the VerCors program verifier. We illustrate how our techniques improve scalability through a large number of experiments. Using our techniques on a set of typical GPU kernels, we achieve a reduction of verification time by, on average, a factor of 9, with outliers being up to 150 times faster. Additionally, applying these techniques to earlier experiments and an earlier case study of a radio telescope pipeline permitted the verification of results which were previously unobtainable and significantly reduced the verification time.

cs.SE↗

arXiv2026

Deductive Verification of Weak Memory Programs with View-based Protocols (extended version)

Concurrent programming under weak memory concurrency faces substantial challenges to ensure correctness due to program behaviors that cannot be explained by thread interleaving, a.k.a. sequential consistency. While several program logics are proposed to reason about weak memory concurrency, their usage has been limited to intricate manual proofs. On the other hand, the VerCors verifier provides a rich toolset for automated deductive verification for sequential consistency. In this paper, we bridge this gap for automated deductive verification of weak memory concurrent programs with the VerCors deductive verification tool. We propose an approach to encode weak memory concurrency in VerCors. We develop VerCors-relaxed, where we extend the VerCors atomics support and bring concepts from several protocol automata to encode permission-based separation logics for weak memory concurrency models. To demonstrate the effectiveness of our approach, we encode the relaxed fragment of the SLR program logic, a recent state-of-the-art permission-based separation logic for weak memory concurrency in VerCors-relaxed, our extension of VerCors. We use the SLR encoding on VerCors-relaxed to automatically verify several examples from the literature within realistic performance.

cs.LO↗

arXiv2024

An Evaluation of Massively Parallel Algorithms for DFA Minimization

We study parallel algorithms for the minimization of Deterministic Finite Automata (DFAs). In particular, we implement four different massively parallel algorithms on Graphics Processing Units (GPUs). Our results confirm the expectations that the algorithm with the theoretically best time complexity is not practically suitable to run on GPUs due to the large amount of resources needed. We empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse. Lastly, we introduce a novel algorithm based on partition refinement with an extra parallel partial transitive closure step and show that on specific benchmarks it has better run-time complexity and performs better in practice.

cs.DC↗

arXiv2024

Compact Parallel Hash Tables on the GPU

On the GPU, hash table operation speed is determined in large part by cache line efficiency, and state-of-the-art hashing schemes thus divide tables into cache line-sized buckets. This raises the question whether performance can be further improved by increasing the number of entries that fit in such buckets. Known compact hashing techniques have not yet been adapted to the massively parallel setting, nor have they been evaluated on the GPU. We consider a compact version of bucketed cuckoo hashing, and a version of compact iceberg hashing suitable for the GPU. We discuss the tables from a theoretical perspective, and provide an open source implementation of both schemes in CUDA for comparative benchmarking. In terms of performance, the state-of-the-art cuckoo hashing benefits from compactness on lookups and insertions (most experiments show at least 10-20% increase in throughput), and the iceberg table benefits significantly, to the point of being comparable to compact cuckoo hashing--while supporting performant dynamic operation.

cs.DS↗

arXiv2024

HaliVer: Deductive Verification and Scheduling Languages Join Forces

The HaliVer tool integrates deductive verification into the popular scheduling language Halide, used for image processing pipelines and array computations. HaliVer uses Vercors, a separation logic-based verifier, to verify the correctness of (1) the Halide algorithms and (2) the optimised parallel code produced by \halide when an optimisation schedule is applied to the algorithm. This allows proving complex, optimised code correct while reducing the effort to provide the required verification annotations. For both approaches, the same specification is used. We evaluated the tool on several optimised programs generated from characteristic Halide algorithms, using all but one of the essential scheduling directives available in Halide. Without annotation effort, Haliver proves memory safety in almost all programs. With annotations Haliver, additionally, proves functional correctness properties. We show that the approach is viable and reduces the manual annotation effort by an order of magnitude.

cs.LO↗

arXiv2021

A linear parallel algorithm to compute bisimulation and relational coarsest partitions

The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with $n$ states, $m$ transitions and $|\mathit{Act}|\leq m$ action labels, we provide an algorithm on $max(n,m)$ processors that calculates strong bisimulation in time $O(n+|\mathit{Act}|)$ and space $O(n+m)$. The best-known PRAM algorithm has time complexity $O(n\log n)$ on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

cs.DC↗

arXiv2020

Term Rewriting on GPUs

We present a way to implement term rewriting on a GPU. We do this by letting the GPU repeatedly perform a massively parallel evaluation of all subterms. We find that if the term rewrite systems exhibit sufficient internal parallelism, GPU rewriting substantially outperforms the CPU. Since we expect that our implementation can be further optimized, and because in any case GPUs will become much more powerful in the future, this suggests that GPUs are an interesting platform for term rewriting. As term rewriting can be viewed as a universal programming language, this also opens a route towards programming GPUs by term rewriting, especially for irregular computations.

cs.DC↗

arXiv2019

A simpler O(m log n) algorithm for branching bisimilarity on labelled transition systems

Branching bisimilarity is a behavioural equivalence relation on labelled transition systems that takes internal actions into account. It has the traditional advantage that algorithms for branching bisimilarity are more efficient than all algorithms for other weak behavioural equivalences, especially weak bisimilarity. With $m$ the number of transitions and $n$ the number of states, the classic $O(m n)$ algorithm was recently replaced by an $O(m (\log \lvert \mathit{Act}\rvert + \log n))$ algorithm, which is unfortunately rather complex. This paper combines its ideas with the ideas from Valmari. This results in a simpler algorithm with complexity $O(m \log n)$. Benchmarks show that this new algorithm is also faster and often far more memory efficient than its predecessors. This makes it the best option for branching bisimulation minimisation and preprocessing for weak bisimulation of LTSs.

cs.LO↗

arXiv2017

Analysing the Performance of GPU Hash Tables for State Space Exploration

In the past few years, General Purpose Graphics Processors (GPUs) have been used to significantly speed up numerous applications. One of the areas in which GPUs have recently led to a significant speed-up is model checking. In model checking, state spaces, i.e., large directed graphs, are explored to verify whether models satisfy desirable properties. GPUexplore is a GPU-based model checker that uses a hash table to efficiently keep track of already explored states. As a large number of states is discovered and stored during such an exploration, the hash table should be able to quickly handle many inserts and queries concurrently. In this paper, we experimentally compare two different hash tables optimised for the GPU, one being the GPUexplore hash table, and the other using Cuckoo hashing. We compare the performance of both hash tables using random and non-random data obtained from model checking experiments, to analyse the applicability of the two hash tables for state space exploration. We conclude that Cuckoo hashing is three times faster than GPUexplore hashing for random data, and that Cuckoo hashing is five to nine times faster for non-random data. This suggests great potential to further speed up GPUexplore in the near future.

cs.DC↗

arXiv2017

On the Scalability of the GPUexplore Explicit-State Model Checker

The use of graphics processors (GPUs) is a promising approach to speed up model checking to such an extent that it becomes feasible to instantly verify software systems during development. GPUexplore is an explicit-state model checker that runs all its computations on the GPU. Over the years it has been extended with various techniques, and the possibilities to further improve its performance have been continuously investigated. In this paper, we discuss how the hash table of the tool works, which is at the heart of its functionality. We propose an alteration of the hash table that in isolated experiments seems promising, and analyse its effect when integrated in the tool. Furthermore, we investigate the current scalability of GPUexplore, by experimenting both with input models of varying sizes and running the tool on one of the latest GPUs of NVIDIA.

cs.DC↗

arXiv2016

Proceedings Second Graphs as Models Workshop

Graphs are used as models in all areas of computer science: examples are state space graphs, control flow graphs, syntax graphs, UML-type models of all kinds, network layouts, social networks, dependency graphs, and so forth. Once such graphical models are constructed, they can be analysed and transformed to verify their correctness within a domain, discover new properties, or produce new equivalent and/or optimised versions. Graphs as Models' main focus is the exchange and collaboration of researchers from different backgrounds. The workshop serves as platform to boost inter- and transdisciplinary research and wants to serve as leeway for new ideas. Thus, besides classical research presentations, the workshop is highly geared toward numerous interactive sessions. The second edition of the Graphs as Models workshop was held on 2-3 June 2016 in Eindhoven, The Netherlands, colocated with the 19th European Joint Conferences on Theory and Practice of Software (ETAPS 2016).

cs.DS↗

arXiv2016

An O(m log n) Algorithm for Stuttering Equivalence and Branching Bisimulation

We provide a new algorithm to determine stuttering equivalence with time complexity $O(m \log n)$, where $n$ is the number of states and $m$ is the number of transitions of a Kripke structure. This algorithm can also be used to determine branching bisimulation in $O(m(\log |\mathit{Act}|+ \log n))$ time where $\mathit{Act}$ is the set of actions in a labelled transition system. Theoretically, our algorithm substantially improves upon existing algorithms which all have time complexity $O(m n)$ at best. Moreover, it has better or equal space complexity. Practical results confirm these findings showing that our algorithm can outperform existing algorithms with orders of magnitude, especially when the sizes of the Kripke structures are large. The importance of our algorithm stretches far beyond stuttering equivalence and branching bisimulation. The known $O(m n)$ algorithms were already far more efficient (both in space and time) than most other algorithms to determine behavioural equivalences (including weak bisimulation) and therefore it was often used as an essential preprocessing step. This new algorithm makes this use of stuttering equivalence and branching bisimulation even more attractive.

cs.LO↗

arXiv2015

Confluence Detection for Transformations of Labelled Transition Systems

The development of complex component software systems can be made more manageable by first creating an abstract model and then incrementally adding details. Model transformation is an approach to add such details in a controlled way. In order for model transformation systems to be useful, it is crucial that they are confluent, i.e. that when applied on a given model, they will always produce a unique output model, independent of the order in which rules of the system are applied on the input. In this work, we consider Labelled Transition Systems (LTSs) to reason about the semantics of models, and LTS transformation systems to reason about model transformations. In related work, the problem of confluence detection has been investigated for general graph structures. We observe, however, that confluence can be detected more efficiently in special cases where the graphs have particular structural properties. In this paper, we present a number of observations to detect confluence of LTS transformation systems, and propose both a new confluence detection algorithm and a conflict resolution algorithm based on them.

cs.LO↗

arXiv2014

Proceedings 3rd Workshop on GRAPH Inspection and Traversal Engineering

These are the proceedings of the Third Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014), which took place on April 5, 2014 in Grenoble, France, as a satellite event of the 17th European Joint Conferences on Theory and Practice of Software (ETAPS 2014). The aim of GRAPHITE is to foster the convergence on research interests from several communities dealing with graph analysis in all its forms in computer science, with a particular attention to software development and analysis. Graphs are used to represent data and processes in many application areas, and they are subjected to various computational algorithms in order to analyze them. Just restricting the attention to the analysis of software, graph analysis algorithms are used, for instance, to verify properties using model checking techniques that explore the system's state space graph or static analysis techniques based on control flow graphs. Further application domains include games, planning, and network analysis. Very often, graph problems and their algorithmic solutions have common characteristics, independent of their application domain. The goal of this event is to gather scientists from different communities, who do research on graph analysis algorithms, such that awareness of each others' work is increased. More information can be found at http://sysma.imtlucca.it/graphite.

cs.LO↗

arXiv2013

Proceedings 2nd Workshop on GRAPH Inspection and Traversal Engineering

These are the proceedings of the Second Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2013), which took place on March 24, 2013 in Rome, Italy, as a satellite event of the 16th European Joint Conferences on Theory and Practice of Software (ETAPS 2013). The topic of the GRAPHITE workshop is graph analysis in all its forms in computer science. Graphs are used to represent data in many application areas, and they are subjected to various computational algorithms in order to acquire the desired information. These graph algorithms tend to have common characteristics, such as duplicate detection to guarantee their termination, independent of their application domain. Over the past few years, it has been shown that the scalability of such algorithms can be dramatically improved by using, e.g., external memory, by exploiting parallel architectures, such as clusters, multi-core CPUs, and graphics processing units, and by using heuristics to guide the search. Novel techniques to further scale graph search algorithms, and new applications of graph search are within the scope of this workshop. Another topic of interest of the event is more related to the structural properties of graphs: which kind of graph characteristics are relevant for a particular application area, and how can these be measured? Finally, any novel way of using graphs for a particular application area is on topic. The goal of this event is to gather scientists from different communities, such as model checking, artificial intelligence planning, game playing, and algorithm engineering, who do research on graph search algorithms, such that awareness of each others' work is increased.

cs.DS↗

arXiv2012

Proceedings First Workshop on GRAPH Inspection and Traversal Engineering

These are the proceedings of the First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012), which took place on April 1, 2012 in Tallinn, Estonia, as a satellite event of the 15th European Joint Conferences on Theory and Practice of Software (ETAPS 2012). The topic of the GRAPHITE workshop is graph search in all its forms in computer science. Graph search algorithms tend to have common characteristics, such as duplicate state detection, independent of their application domain. Over the past few years, it has been shown that the scalability of such algorithms can be dramatically improved by using, e.g., external memory, by exploiting parallel architectures, such as clusters, multi-core CPUs, and graphics processing units, and by using heuristics to guide the search. The goal of this event is to gather scientists from different communities, such as model checking, artificial intelligence planning, game playing, and algorithm engineering, who do research on graph search algorithms, such that awareness of each others' work is increased.

cs.DS↗

arXiv2011

The HIVE Tool for Informed Swarm State Space Exploration

Swarm verification and parallel randomised depth-first search are very effective parallel techniques to hunt bugs in large state spaces. In case bugs are absent, however, scalability of the parallelisation is completely lost. In recent work, we proposed a mechanism to inform the workers which parts of the state space to explore. This mechanism is compatible with any action-based formalism, where a state space can be represented by a labelled transition system. With this extension, each worker can be strictly bounded to explore only a small fraction of the state space at a time. In this paper, we present the HIVE tool together with two search algorithms which were added to the LTSmin tool suite to both perform a preprocessing step, and execute a bounded worker search. The new tool is used to coordinate informed swarm explorations, and the two new LTSmin algorithms are employed for preprocessing a model and performing the individual searches.

cs.SE↗