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

Productivity impacts of infrastructure investment in the Netherlands 1853-1913

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.

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.Comment: In Proceedings EXPRESS/SOS 2019, arXiv:1908.0821

Output responses to infrastructure investment in the Netherlands, 1850-1913

This paper combines a new historical data set regarding capital formation in infrastructure in the Netherlands in the nineteenth century with data-oriented econometric techniques aimed at testing the causal relationship between these infrastructural investments and economic growth. The resulting vector autoregression (VAR) model is analysed further with impulse response analysis. The results show that the time series characteristics of both capital formation and GDP are trend stationary, which is a fundamental difference with their twentieth century counterparts. The paper finds strong evidence of both a long term and medium term or short term impact. In the short run positive expenditure effects are partly offset bu negative transitional dynamics. To fine tune the analysis we have exploited the possibility to disaggregate the data set in basic and complementary infrastructure investment. Whereas the effect on output is significantly positive for basic infrastructure investment, it is absent for complementary infrastructure investment.

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.Comment: In Proceedings MARS 2017, arXiv:1703.0581

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.Comment: 22 pages, in LNCS format, Submitted to QEST'1

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

Computing Minimal Distinguishing Hennessy-Milner Formulas is NP-Hard, but Variants are Tractable

We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is NP-complete. However, we can provide polynomial algorithms, if minimality is formulated as the minimal number of nested modalities, and it can even be extended by recursively requiring a minimal number of nested negations. A prototype implementation shows that the generated formulas are much smaller than those generated by the method introduced by Cleaveland

Computing minimal distinguishing Hennessy-Milner formulas is NP-hard, but variants are tractable

We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is NP-complete. However, we can provide polynomial algorithms, if minimality is formulated as the minimal number of nested modalities, and it can even be extended by recursively requiring a minimal number of nested negations. A prototype implementation shows that the generated formulas are much smaller than those generated by the method introduced by Cleaveland.Comment: Accepted at CONCUR 202