Distributed Computation of Fixed Points on Dependency Graphs

A Distributed Fixed-Point Algorithm for Extended Dependency Graphs*

“…A dependency graph, consisting of a finite set of nodes and hyper-edges with multiple target nodes, is an abstract framework for efficient minimum fixed-point computation over the node assignments that assign to each node the value 0 or 1. It has a variety of usages, including model checking [7,8,9] and equivalence checking [12]. Apart from formal verification, dependency graphs are also used to solve games based e.g.…”

“…The advantage of the local algorithm is that it only needs to compute the values for a subset of the nodes in order to conclude about the assignment value for a given node of the graph. In practise, the local algorithm is superior to the global one [7] and to further boost its performance, we recently suggested a distributed implementation of the local algorithm with preliminary experimental results [12] conducted for weak bisimulation and simulation checking of CCS processes.…”

“…Our contributions. Neither the original paper by Liu and Smolka [6] nor the recent distributed implementation [12] handle the problem of negation in dependency graphs as this can break the monotonicity in the iterative evaluation of the fixed points. In our work, we extend dependency graphs with so-called negation edges, define a sufficient condition for the existence of unique fixed points and design an efficient algorithm for their computation, hence allowing us to encode richer properties rather than just plain equivalence checking or negation-free model checking.…”

“…Our approach relies on reducing a variety of verification problems into extended dependency graphs and then on employing our optimized and efficient distributed implementation, as e.g. demonstrated on CTL model checking of Petri nets presented in this paper or on bisimulation checking of CCS processes [12].…”

Abstract Dependency Graphs and Their Application to Model Checking

“…Dependency Graphs (DG) [1] have demonstrated a wide applicability with respect to verification and synthesis of reactive systems, e.g. checking behavioural equivalences between systems [2], model checking systems with respect to temporal logical properties [3][4][5], as well as synthesizing missing components of systems [6]. The DG approach offers a general and often performance-optimal way to solve these problem.…”