We address the problem of verifying programs manipulating one-selector linked data structures. We propose and study in detail an application of counter automata as an accurate abstract model for this problem. We let control states of the counter automata correspond to abstract heap graphs where list segments without sharing are collapsed, and use counters to keep track of the number of elements in these segments. As a significant theoretical result, we show that the obtained counter automata are bisimilar to the original programs. Moreover, from a practical point of view, our translation allows one to apply efficient automatic analysis techniques and tools developed for counter automata (integer programs) in order to verify both safety as well as termination of list-manipulating programs. As another This work is a full and revised version of the extended abstract [10] published in Proceedings of CAV'06. Form Methods Syst Des (2011) 38: 158-192 159 theoretical contribution, we prove that if the control of the generated counter automata does not contain nested loops (i.e., these automata are flat), both safety and termination are decidable for the original programs. Subsequently, we generalise our counter-automata-based model to keep track of ordering properties over lists storing ordered data. Finally, we show effectiveness of our approach by verifying automatically safety as well as termination of several sorting programs.

Abstract. We address the problem of automatic verification of programs with dynamic data structures. We consider the case of sequential, non-recursive programs manipulating 1-selector-linked structures such as traditional linked lists (possibly sharing their tails) and circular lists. We propose an automata-based approach for a symbolic verification of such programs using the regular model checking framework. Given a program, the configurations of the memory are systematically encoded as words over a suitable finite alphabet, potentially infinite sets of configurations are represented by finite-state automata, and statements of the program are automatically translated into finite-state transducers defining regular relations between configurations. Then, abstract regular model checking techniques are applied in order to automatically check safety properties concerning the shape of the computed configurations or relating the input and output configurations. For this particular purpose, we introduce new techniques for the computation of abstractions of the set of reachable configurations and to refine these abstractions if spurious counterexamples are detected. Finally, we present experimental results showing the applicability of the approach and its efficiency.

Abstract. We propose an algorithm to find a counterexample to some property in a finite state program. This algorithm is derived from SPIN's one, but it finds a counterexample faster than SPIN does. In particular it still works in linear time. Compared with SPIN's algorithm, it requires only one additional bit per state stored. We further propose another algorithm to compute a counterexample of minimal size. Again, this algorithm does not use more memory than SPIN does to approximate a minimal counterexample. The cost to find a counterexample of minimal size is that one has to revisit more states than SPIN. We provide an implementation and discuss experimental results.

Abstract. In this paper, we propose an algorithm to compute a counterexample of minimal size to some property in a finite state program, using the same programmation constraints than SPIN. This algorithm uses nested Breadth-first searches guided by priority queues. This algorithm works in quadratic time and is linear in memory,

Abstract-Given a Parametric Timed Automaton (PTA) A and a reference valuation for timings, the Inverse Method (IM) synthesizes a constraint around the reference valuation where A behaves in the same time-abstract manner. This provides us with a quantitative measure of robustness of the behavior of A around the reference valuation. We show in this paper how IM can be applied in a specific way to treat the robustness of scheduling systems. We also explain how to use the method in order to synthesize large zones of the timing parameter space where the system is guaranteed to be schedulable. We illustrate the method on several examples of the literature as well as a case study originating from an industrial design project.

Abstract. We address the verification problem of programs manipulating oneselector linked data structures. We propose a new automated approach for checking safety and termination for these programs. Our approach is based on using counter automata as accurate abstract models: control states correspond to abstract heap graphs where list segments without sharing are collapsed, and counters are used to keep track of the number of elements in these segments. This allows to apply automatic analysis techniques and tools for counter automata in order to verify list programs. We show the effectiveness of our approach, in particular by verifying automatically termination of some sorting programs.