Incremental Model Checking for Decomposable Structures

. Assume we are given a transition system which is composed from several well identified components. We propose a method which allows us to reduce the model checking of formulas in the complex system to model checking of derived formulas in Monadic Second Order Logic in the components. Our method applies to all practically used hardware specification languages, although at a certain cost. The basic idea goes back to a method proposed first by Feferman and Vaught in 1959, which we adapt and generalize to the specific context of model checking of transition systems. Our method allows for a precise definition of incremental model checking. We give also estimates on when our incremental method starts to be better than traditional methods. 1 Introduction In hardware verification (but not only) we find the following situation: We are given a mathematical model of a finite state device in form of a finite relational structure A (transition system) and a formalized property OE. Usually OE is ..

Incremental Model Checking for Fixed Point Properties on Decomposable Structures

, April 1995 Abstract. Assume we are given a transition system which is composed from several well identified components. We propose a method which allows us to reduce the model checking of Safety, Reachability and Liveness Properties (expressible in fixed point logic) in the complex system to model checking of derived formulas in Transitive Closure Logic in the components, provided the complex systems is a \Phi-sum of its components. The basic idea goes back to a method proposed first by Feferman and Vaught in 1959, which we generalize to Transitive Closure Logic TC 1 . The generalization for Fixed Point Logic LFP 1 is due to U. Bosse. We adapt the method to the specific context of model checking of transition systems. Our method allows for a precise definition of incremental model checking. We give also estimates on when our incremental method starts to be better than traditional methods. 1 Introduction In hardware verification we find the following situation: We are given a mat..

Effective optimization with weighted automata on decomposable trees

In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effectively derived problems, defined in the same logic, on its components with some additional post-processing. The approach originates from a method, proposed first by Feferman and Vaught in 1959, which we adapt and generalize. We adapt the method to the case of (fragments of) Weighted Monadic Second Order Logic and generalize it to the case of sum-like labeled trees rather than disjoint union and product. The main result of the paper may be applied in the wide range of optimization problems, such as critical path analysis or project planning, network optimization, generalized assignment problem, routing and scheduling as well as in the modern document languages like XML, image processing and compression, probabilistic systems or speech-to-text processing

An estimate of the objective function optimum for the network Steiner problem

A complete weighted graph, (Formula presented.) , is considered. Let (Formula presented.) be some subset of vertices and, by definition, a Steiner tree is any tree in the graph G such that the set of the tree vertices includes set (Formula presented.). The Steiner tree problem consists of constructing the minimum-length Steiner tree in graph G, for a given subset of vertices (Formula presented.) The effectively computable estimate of the minimal Steiner tree is obtained in terms of the mean value and the variance over the set of all Steiner trees. It is shown that in the space of the lengths of the graph edges, there exist some regions where the obtained estimate is better than the minimal spanning tree-based one