We tackle the problem of graph transformation with a particular focus on node cloning. We propose a new approach to graph rewriting where nodes can be cloned zero, one or more times. A node can be cloned together with all its incident edges, with only its outgoing edges, with only its incoming edges or with none of its incident edges. We thus subsume previous works such as the sesqui-pushout, the heterogeneous pushout and the adaptive star grammars approaches. A rewrite rule is defined as a span where the right-hand and left-hand sides are graphs while the interface is a polarized graph. A polarized graph is a graph endowed with some annotations on nodes. The way a node is cloned is indicated by its polarization annotation. We use these annotations for designing graph transformation with polarized cloning. We show how a clone of a node can be built according to the different possible polarizations and define a rewrite step as a final pullback complement followed by a pushout. This is called the polarized sesqui-pushout approach. We also provide an algorithmic presentation of the proposed graph transformation with polarized cloning.
In @cite_0 , the sesqui-pushout approach has been compared to the classical double pushout and single pushout approaches. showed that the sesqui-pushout and the DPO approaches coincide under some conditions (see [Proposition 12] CorradiniHHK06 ). They also showed how the sesqui-pushout approach can be simulated by the SPO approach and gave conditions under which a SPO derivation can be simulated by a sesqui-pushout (see [Proposition 13] CorradiniHHK06 ). So, according to Proposition , which shows how to simulate a sesqui-pushout step in our setting, we can infer the same comparisons with respect to DPO and SPO for our graph rewriting definition.
@cite_0
2963115819 2031397756 2092445638 2109783572
Abstract This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages: push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is used to explore the search space without considering any constraints, which can help to get across infeasible regions very quickly and to approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameter setting for the constraint-handling approaches to be applied in the pull stage. Then, a modified form of a constrained multi-objective evolutionary algorithm (CMOEA), with improved epsilon constraint-handling, is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs and a real-world optimization problem are used to test the proposed PPS (PPS-MOEA D) and state-of-the-art CMOEAs, including MOEA D-IEpsilon, MOEA D-Epsilon, MOEA D-CDP, MOEA D-SR, C-MOEA D and NSGA-II-CDP. The comprehensive experimental results show that the proposed PPS-MOEA D achieves significantly better performance than the other six CMOEAs on most of the tested problems, which indicates the superiority of the proposed PPS method for solving CMOPs. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. Abstract The purpose of the present paper is twofold: Firstly, show that it is possible to rewrite graphs in a way equivalent to, and in fact slightly more powerful than that of Ehrig, Pfender and Schneider (1973), which has, since then, been developed mainly by the Berlin school. Our method consists in using a single push-out of partial morphisms and is described in Section 3. Section 1 is devoted to the elementary definitions concerning graphs and related terms. Section 2 contains the set-theoretic prerequisites for the sequel but the proofs have been moved into an appendix, for easier reading. Secondly, we indicate in Section 4 why this method is not really fit for rewriting graphs that represent collapsed terms (i.e., sharing common subterms) and we introduce pushouts of total functions, which are not morphisms everywhere on their domain. This method is connected to the classical rewriting of the corresponding terms. The adequacy of these new rewriting rules is then tested to prove a local confluence criterion a la Knuth-Bendix (1970) in Section 5, the proof of which turns out to be very short. This paper introduces and studies the class of differential variational inequalities (DVIs) in a finite-dimensional Euclidean space. The DVI provides a powerful modeling paradigm for many applied problems in which dynamics, inequalities, and discontinuities are present; examples of such problems include constrained time-dependent physical systems with unilateral constraints, differential Nash games, and hybrid engineering systems with variable structures. The DVI unifies several mathematical problem classes that include ordinary differential equations (ODEs) with smooth and discontinuous right-hand sides, differential algebraic equations (DAEs), dynamic complementarity systems, and evolutionary variational inequalities. Conditions are presented under which the DVI can be converted, either locally or globally, to an equivalent ODE with a Lipschitz continuous right-hand function. For DVIs that cannot be so converted, we consider their numerical resolution via an Euler time-stepping procedure, which involves the solution of a sequence of finite-dimensional variational inequalities. Borrowing results from differential inclusions (DIs) with upper semicontinuous, closed and convex valued multifunctions, we establish the convergence of such a procedure for solving initial-value DVIs. We also present a class of DVIs for which the theory of DIs is not directly applicable, and yet similar convergence can be established. Finally, we extend the method to a boundary-value DVI and provide conditions for the convergence of the method. The results in this paper pertain exclusively to systems with “index” not exceeding two and which have absolutely continuous solutions.