Program Specialization for Verifying Infinite State Systems: An Experimental Evaluation

Abstract

Abstract. We address the problem of the automated verification of temporal properties of infinite state reactive systems. We present some improvements of a verification method based on the specialization of constraint logic programs (CLP). First, we reformulate the verification method as a two-phase procedure: (1) in the first phase a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase the specialized program is evaluated by using a bottom-up strategy. In this paper we propose some new strategies for performing program specialization during the first phase. We evaluate the effectiveness of these new strategies, as well as that of some old strategies, by presenting the results of experiments performed on several infinite state systems and temporal properties. Finally, we compare the implementation of our specialization-based verification method with various constraint-based model checking tools. The experimental results show that our method is effective and competitive with respect to the methods used in those other tools.

Using Real Relaxations during Program Specialization

“…However, if ¬ϕ = def ∃x ∈ R (reachable(x) ∧ ∧ ¬safe(x)) holds, then we cannot conclude that ∃x ∈ Z (reachable(x) ∧ ∧ ¬safe(x)) holds. Now, as indicated in the literature (see, for instance, [17,19,29,30,31]) the verification of infinite state reactive systems can be done via program specialization and, in particular, in [19] we proposed a technique consisting of the following two steps: (Step 1) the specialization of the constraint logic program that encodes the given system, with respect to the query that encodes the property to be verified, and (Step 2) the construction of the perfect model of the specialized program.…”

“…The problem of designing suitable unfolding and generalization operators has been addressed in many papers and various solutions have been proposed in the literature (see, for instance, [16,19,31] and [28] for a survey in the case of logic programs). In this paper we will not focus on this aspect and we will simply assume that we are given: (i) an operator Unfold(δ, P ) which, for every clause δ occurring in a program P , returns a set of clauses derived from δ by applying n (≥ 1) times the unfolding rule R2, and (ii) an operator Gen(c ∧ ∧ A, Defs) which, for every constraint c, atom A with vars(c) ⊆ vars(A), and set Defs of the definition clauses introduced so far by Rule R1 during the Specialization Strategy, returns a constraint g that is more general than c, that is: (i) vars(g) ⊆ vars(c) and (ii) c ⊑ R g. An example of the generalization operator Gen will be presented in Section 5.…”

“…In this section we will take into consideration safety properties, but our technique can be applied to more complex properties, such as CTL temporal properties [9,19]. A reactive system is said to be safe if from every initial state it is not possible to reach, by zero or more applications of the transition relation, a state, called an unsafe state, satisfying an undesired property.…”

“…It has been shown in [19] that the termination of the bottom-up construction of the perfect model of a program can be improved by first specializing the program with respect to the query of interest. In this paper, we use a variant of the specialization-based method presented in [19] which is tailored to the verification of safety properties.…”

“…In this paper we propose a variant of the verification technique introduced in [19]. This variant is based on the specialization of locally stratified CLP(Z) programs and uses a relaxation from the integers to the reals.…”