Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semi-formally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.

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Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

Community structure is one of the most important properties in networks, and community detection has received an enormous amount of attention in recent years. Modularity is by far the most used and best known quality function for measuring the quality of a partition of a network, and many community detection algorithms are developed to optimize it. However, there is a resolution limit problem in modularity optimization methods. In this study, a memetic algorithm, named Meme-Net, is proposed to optimize another quality function, modularity density, which includes a tunable parameter that allows one to explore the network at different resolutions. Our proposed algorithm is a synergy of a genetic algorithm with a hill-climbing strategy as the local search procedure. Experiments on computer-generated and real-world networks show the effectiveness and the multiresolution ability of the proposed method.

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Memetic algorithm for community detection in networks.

Handbook of Approximation: Algorithms and Metaheuristics

Endometrial cancer is the most common malignancy of the female genital tract in developed countries. To identify genetic variants associated with endometrial cancer risk, we performed a genome-wide association study involving 1,265 individuals with endometrial cancer (cases) from Australia and the UK and 5,190 controls from the Wellcome Trust Case Control Consortium. We compared genotype frequencies in cases and controls for 519,655 SNPs. Forty seven SNPs that showed evidence of association with endometrial cancer in stage 1 were genotyped in 3,957 additional cases and 6,886 controls. We identified an endometrial cancer susceptibility locus close to HNF1B at 17q12 (rs4430796, P = 7.1 x 10(-10)) that is also associated with risk of prostate cancer and is inversely associated with risk of type 2 diabetes.

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Genome-wide association study identifies a common variant associated with risk of endometrial cancer

Regular model checking is being developed for algorithmic verification of several classes of infinite-state systems whose configurations can be modeled as words over a finite alphabet. Examples include parameterized systems consisting of an arbitrary number of homogeneous finite-state processes connected in a linear or ring-formed topology, and systems that operate on queues, stacks, integers, and other linear data structures. The main idea is to use regular languages as the representation of sets of configurations, and finite-state transducers to describe transition relations. In general, the verification problems considered are all undecidable, so the work has consisted in developing semi-algorithms, and decidability results for restricted cases. This paper provides a survey of the work that has been performed so far, and some of its applications.

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A Survey of Regular Model Checking

In this paper, we present an approach for algorithmic verification of infinite-state systems with a parameterized tree topology. Our work is a generalization of regular model checking, where we extend the work done with strings toward trees. States are represented by trees over a finite alphabet, and transition relations by regular, structure preserving relations on trees. We use an automata theoretic method to compute the transitive closure of such a transition relation. Although the method is incomplete, we present sufficient conditions to ensure termination.We have implemented a prototype for our algorithm and show the result of its application on a number of examples.

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Regular Tree Model Checking

We consider verification of safety properties for parameterized systems of timed processes, so called timed networks. A timed network consists of a finite state process, called a controller, and an arbitrary set of identical timed processes. In a previous work, we showed that checking safety properties is decidable in the case where each timed process is equipped with a single real-valued clock. It was left open whether the result could be extended to multi-clock timed networks. We show that the problem becomes undecidable when each timed process has two clocks. On the other hand, we show that the problem is decidable when clocks range over a discrete time domain. This decidability result holds when processes have any finite number of clocks.

Multi-clock timed networks

In this paper, we present an approach for algorithmic verification of infinite-state systems with a parameterized tree topology. Our work is a generalization of regular model checking, where we extend the work done with strings toward trees. States are represented by trees over a finite alphabet, and transition relations by regular, structure preserving relations on trees. We use an automata theoretic method to compute the transitive closure of such a transition relation. Although the method is incomplete, we present sufficient conditions to ensure termination. We have implemented a prototype for our algorithm and show the result of its application on a number of examples.

Regular tree model checking

We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fir ...

Dense-timed petri nets: checking zenoness, token liveness and boundedness

We consider verification of safety properties for concurrent real-timed systems modelled as timed Petri nets, by performing symbolic forward reachability analysis. We introduce a formalism, called region generators for representing sets of markings of timed Petri nets. Region generators characterize downward closed sets of regions, and provide exact abstractions of sets of reachable states with respect to safety properties. We show that the standard operations needed for performing symbolic reachability analysis are computable for region generators. Since forward reachability analysis is necessarily incomplete, we introduce an acceleration technique to make the procedure terminate more often on practical examples. We have implemented a prototype for analyzing timed Petri nets and used it to verify a parameterized version of Fischer’s protocol and a producer-consumer protocol. We also used the tool to extract finite-state abstractions of these protocols.

Pritha Mahata

Papers

Regular Tree Model Checking

Multi-clock timed networks

Regular tree model checking

Dense-timed petri nets: checking zenoness, token liveness and boundedness

Forward reachability analysis of timed Petri nets