The uniform verification problem for parameterized systems is to determine whether a temporal property is true for every instance of the system which is composed of an arbitrary number of homogeneous processes. We consider some aspects of the inductionbased technique which assumes the construction of finite invariants of such systems. An invariant process is one which is greater (with respect t...

We present some sufficient conditions for the existence of a continuous multi-utility representation of a preorder on a topological space (X, τ) (i.e., for the existence of a family F of continuous increasing realvalued functions on the preordered topological space (X, τ, ) such that, for every pair of elements (x, y) ∈ X×X, x y ⇔ f(x) ≤ f(y) ∀f ∈ F). Such conditions are based on the concept of...

An inequality preorder is defined as a complete preorder on a simplex which satisfies the properties of continuity and strict Schur-convexity (the mathematical equivalent of Dalton's "principle of transfers"). The paper shows that it is possible to aggregate individual inequality preorders into a collective one if we are interested in continuous anonymous aggregation rules that respect unanimit...

In this paper we present a new functional traversal abstraction for processing OO data structures that decomposes traversal computation into three function objects and a traversal control function. Function objects compute and combine values over a general traversal while the control function allows programmers to limit the extent of a traversal. Our new abstraction is supported by a Java libra...

The finite satisfiability problem for two-variable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is complete for EXPSPACE. As a consequence, the same upper bound applies to the case of two linear orders. ...

This work presents a minimization algorithm. The algorithm receives a Kripke structure M and returns the smallest structure that is simulation equivalent to M. The simulation equivalencerelation is weaker than bisimulation but stronger than the simulation preorder. It strongly preserves ACTL and LTL (as sub-logics of ACTL). We show that every structure M has a unique up to isomorphism reduced s...

In this paper we consider Milner’s calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We define operational notions of preorder and equivalence as probabilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

We propose a general approach for defining behavioural preorders over process terms as the maximal pre–congruences induced by basic observables. We will consider three of these, that provide information about the initial communication capabilities of processes and about the possibility that processes get engaged in divergent computations. We show that the pre–congruences induced by our basic ob...

We describe a framework for compositional veri cation of nite state processes The framework is based on two ideas a subset of the logic CTL for which satisfaction is preserved under composition and a preorder on structures which captures the relation between a component and a system containing the component Satisfaction of a formula in the logic corresponds to being below a particular structure...

We describe a framework for compositional verification of finite state processes. The framework is based on two ideas: a subset of the logic CTL for which satisfaction is preserved under composition; and a preorder on structures which captures the relation between a component and a system containing the component. Satisfaction of a formula in the logic corresponds to being below a particular st...