Laura Bozzelli

Pushdown module checking

Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depends on the interaction with their environment. The model checking problem for finite–state open systems (called module checking) has been intensively studied in the literature. In this paper, we focus on open pushdown systems and we study the related model–checking problem (pushdown module checking, for short) with respect to properties expressed by CTL and CTL* formulas. We show that pushdown module checking against CTL (resp., CTL*) is 2Exptime-complete (resp., 3Exptime-complete). Moreover, we prove that for a fixed CTL* formula, the problem is Exptime-complete.

Verification of gap-order constraint abstractions of counter systems

We investigate verification problems for gap-order constraint systems (GCS), an (infinitely-branching) abstract model of counter machines, in which constraints (over Z) between the variables of the source state and the target state of a transition are gap-order constraints (GC) [32]. GCS extend monotonicity constraint systems [7], integral relation automata [16], and constraint automata in [19]. First, we address termination and fairness analysis of GCS. Since GCS are infinitely-branching, termination does not imply strong termination, i.e. the existence of an upper bound on the lengths of the runs from a given state. We show that the termination problem, the strong termination problem, and the fairness problem for GCS (the latter consisting in checking the existence of infinite runs in GCS satisfying acceptance conditions a la Buchi) are decidable and Pspace-complete. Moreover, for each control location of the given GCS, one can build a GC representation of the set of counter variable valuations from which termination (resp., strong termination, resp., fairness) does not hold (resp., does not hold, resp., does hold). Next, we consider a constrained branching-time logic, GCCTL^@?, obtained by enriching CTL^@? with GC, thus enabling expressive properties and subsuming the setting of [16]. We establish that, while model-checking GCS against the universal fragment of GCCTL^@? is undecidable, model-checking against the existential fragment, and satisfiability of both the universal and existential fragments are instead decidable and Pspace-complete (note that the two fragments are not dual since GC are not closed under negation). Moreover, our results imply Pspace-completeness of known verification problems that were shown to be decidable in [16] with no elementary upper bounds.

Complexity results on branching-time pushdown model checking

The model checking problem of pushdown systems (PMC problem, for short) against standard branching temporal logics has been intensively studied in the literature. In particular, for the modal μ-calculus, the most powerful branching temporal logic used for verification, the problem is known to be Exptime-complete (even for a fixed formula). The problem remains Exptime-complete also for the logic CTL, which corresponds to a fragment of the alternation-free modal μ-calculus. However, the exact complexity in the size of the pushdown system (for a fixed CTL formula) is an open question: it lies somewhere between Pspace and Exptime. To the best of our knowledge, the PMC problem for CTL* has not been investigated so far. In this paper, we show that this problem is 2Expspace-complete. Moreover, we prove that the program complexity of the PMC problem against CTL (i.e., the complexity of the problem in terms of the size of the system) is Exptime-complete.

Interval Temporal Logic Model Checking: The Border Between Good and Bad HS Fragments

The model checking problem has thoroughly been explored in the context of standard point-based temporal logics, such as LTL, CTL, and CTL

Foundations of Boolean Stream Runtime Verification

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Strong termination for gap-order constraint abstractions of counter systems

, whereas model checking for interval temporal logics has been brought to the attention only very recently. In this paper, we prove that the model checking problem for the logic of Allens relations started-by and finished-by is highly intractable, as it can be proved to be

On decidability of LTL model checking for process rewrite systems

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