arXiv subjects

Jan Friso Groote

Publications and source records attributed to Jan Friso Groote.

33 records · Page 2Linked to original sources

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↗

arXiv2021

Tutorial: Designing Distributed Software in mCRL2

Distributed software is very tricky to implement correctly as some errors only occur in peculiar situations. For such errors testing is not effective. Mathematically proving correctness is hard and time consuming, and therefore, it is rarely done. Fortunately, there is a technique in between, namely model checking, that, if applied with skill, is both efficient and able to find rare errors. In this tutorial we show how to create behavioural models of parallel software, how to specify requirements using modal formulas, and how to verify these. For that we use the mCRL2 language and toolset (https://www.mcrl2.org/). We discuss the design of an evolution of well-known mutual exclusion protocols, and how model checking not only provides insight in their behaviour and correctness, but also guides their design.

cs.LO↗

arXiv2021

Correct and Efficient Antichain Algorithms for Refinement Checking

The notion of refinement plays an important role in software engineering. It is the basis of a stepwise development methodology in which the correctness of a system can be established by proving, or computing, that a system refines its specification. Wang et al. describe algorithms based on antichains for efficiently deciding trace refinement, stable failures refinement and failures-divergences refinement. We identify several issues pertaining to the soundness and performance in these algorithms and propose new, correct, antichain-based algorithms. Using a number of experiments we show that our algorithms outperform the original ones in terms of running time and memory usage. Furthermore, we show that additional run time improvements can be obtained by applying divergence-preserving branching bisimulation minimisation.

cs.LO↗

arXiv2020

A Formally Verified Fail-Operational Safety Concept for Automated Driving

Modern Automated Driving (AD) systems rely on safety measures to handle faults and to bring vehicle to a safe state. To eradicate lethal road accidents, car manufacturers are constantly introducing new perception as well as control systems. Contemporary automotive design and safety engineering best practices are suitable for analyzing system components in isolation, whereas today's highly complex and interdependent AD systems require novel approach to ensure resilience to multi-point failures. We present a holistic safety concept unifying advanced safety measures for handling multiple-point faults. Our proposed approach enables designers to focus on more pressing issues such as handling fault-free hazardous behavior associated with system performance limitations. To verify our approach, we developed an executable model of the safety concept in the formal specification language mCRL2. The model behavior is governed by a four-mode degradation policy controlling distributed processors, redundant communication networks, and virtual machines. To keep the vehicle as safe as possible our degradation policy can reduce driving comfort or AD system's availability using additional low-cost driving channels. We formalized five safety requirements in the modal mu-calculus and proved them against our mCRL2 model, which is intractable to accomplish exhaustively using traditional road tests or simulation techniques. In conclusion, our formally proven safety concept defines a holistic design pattern for designing AD systems.

cs.RO↗

arXiv2020

A symmetric protocol to establish service level agreements

We present a symmetrical protocol to repeatedly negotiate a desired service level between two parties, where the service levels are taken from some totally ordered finite domain. The agreed service level is selected from levels dynamically proposed by both parties and parties can only decrease the desired service level during a negotiation. The correctness of the protocol is stated using modal formulas and its behaviour is explained using behavioural reductions of the external behaviour modulo weak trace equivalence and divergence-preserving branching bisimulation. Our protocol originates from an industrial use case and it turned out to be remarkably tricky to design correctly.

cs.LO↗

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↗

arXiv2019

Distribution of Behaviour into Parallel Communicating Subsystems

The process of decomposing a complex system into simpler subsystems has been of interest to computer scientists over many decades, for instance, for the field of distributed computing. In this paper, motivated by the desire to distribute the process of active automata learning onto multiple subsystems, we study the equivalence between a system and the total behaviour of its decomposition which comprises subsystems with communication between them. We show synchronously- and asynchronously-communicating decompositions that maintain branching bisimilarity, and we prove that there is no decomposition operator that maintains divergence-preserving branching bisimilarity over all LTSs.

cs.FL↗

arXiv2017

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size.

math.PR↗

arXiv2017

Modelling and Verification of a Cluster-tree Formation Protocol Implementation for the IEEE 802.15.4 TSCH MAC Operation Mode

Correct and efficient initialization of wireless sensor networks can be challenging in the face of many uncertainties present in ad hoc wireless networks. In this paper we examine an implementation for the formation of a cluster-tree topology in a network which operates on top of the TSCH MAC operation mode of the IEEE 802.15.4 standard, and investigate it using formal methods. We show how both the mCRL2 language and toolset help us in identifying scenarios where the implementation does not form a proper topology. More importantly, our analysis leads to the conclusion that the cluster-tree formation algorithm has a super linear time complexity. So, it does not scale to large networks.

cs.NI↗

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

Proceedings Workshop on Models for Formal Analysis of Real Systems

This volume contains the proceedings of MARS 2015, the first workshop on Models for Formal Analysis of Real Systems, held on November 23, 2015 in Suva, Fiji, as an affiliated workshop of LPAR 2015, the 20th International Conference on Logic for Programming, Artificial Intelligence and Reasoning. The workshop emphasises modelling over verification. It aims at discussing the lessons learned from making formal methods for the verification and analysis of realistic systems. Examples are: (1) Which formalism is chosen, and why? (2) Which abstractions have to be made and why? (3) How are important characteristics of the system modelled? (4) Were there any complications while modelling the system? (5) Which measures were taken to guarantee the accuracy of the model? We invited papers that present full models of real systems, which may lay the basis for future comparison and analysis. An aim of the workshop is to present different modelling approaches and discuss pros and cons for each of them. Alternative formal descriptions of the systems presented at this workshop are encouraged, which should foster the development of improved specification formalisms.

cs.LO↗

arXiv2015

Exact Real Arithmetic with Perturbation Analysis and Proof of Correctness

In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to guarantee the correctness of the approximations. Moreover, we develop and apply a perturbation analysis method to show that our approximation procedures only recompute expressions when unavoidable. In the last decade, various theories have been developed and implemented to realize real computations with arbitrary precision. Proof of correctness for existing approaches typically consider basic algebraic operations, whereas detailed arguments about transcendental operations are not available. Another important observation is that in each approach some expressions might require iterative computations to guarantee the desired precision. However, no formal reasoning is provided to prove that such iterative calculations are essential in the approximation procedures. In our approximations of real functions, we explicitly relate the precision of the inputs to the guaranteed precision of the output, provide full proofs and a precise analysis of the necessity of iterations.

math.NA↗

arXiv2015

Communication Patterns in Mean Field Models for Wireless Sensor Networks

Wireless sensor networks are usually composed of a large number of nodes, and with the increasing processing power and power consumption efficiency they are expected to run more complex protocols in the future. These pose problems in the field of verification and performance evaluation of wireless networks. In this paper, we tailor the mean-field theory as a modeling technique to analyze their behavior. We apply this method to the slotted ALOHA protocol, and establish results on the long term trends of the protocol within a very large network, specially regarding the stability of ALOHA-type protocols.

cs.PF↗

arXiv2004

Lock-free dynamic hash tables with open addressing

We present an efficient lock-free algorithm for parallel accessible hash tables with open addressing, which promises more robust performance and reliability than conventional lock-based implementations. ``Lock-free'' means that it is guaranteed that always at least one process completes its operation within a bounded number of steps. For a single processor architecture our solution is as efficient as sequential hash tables. On a multiprocessor architecture this is also the case when all processors have comparable speeds. The algorithm allows processors that have widely different speeds or come to a halt. It can easily be implemented using C-like languages and requires on average only constant time for insertion, deletion or accessing of elements. The algorithm allows the hash tables to grow and shrink when needed. Lock-free algorithms are hard to design correctly, even when apparently straightforward. Ensuring the correctness of the design at the earliest possible stage is a major challenge in any responsible system development. In view of the complexity of the algorithm, we turned to the interactive theorem prover PVS for mechanical support. We employ standard deductive verification techniques to prove around 200 invariance properties of our algorithm, and describe how this is achieved with the theorem prover PVS.

cs.DC↗