The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems

International audienceBounded languages have recently proved to be an important class of languages for the analysis of Turing-powerful models. For instance, bounded context-free languages are used to under-approximate the behav-iors of recursive programs. Ginsburg and Spanier have shown in 1966 that a bounded language L ⊆ a * 1 · · · a * d is context-free if, and only if, its Parikh image is a stratifiable semilinear set. However, the question whether a semilinear set is stratifiable, hereafter called the stratifiability problem, was left open, and remains so. In this paper, we give a partial answer to this problem. We focus on semilinear sets that are given as finite systems of linear inequalities, and we show that stratifiability is coNP-complete in this case. Then, we apply our techniques to the context-freeness problem for flat counter systems, that asks whether the trace language of a counter system intersected with a bounded regular language is context-free. As main result of the paper, we show that this problem is coNP-complete

Abstract Regular Model Checking

International audienceWe propose abstract regular model checking as a new generic technique for verification of parametric and infinite-state systems. The technique combines the two approaches of regular model checking and verification by abstraction. We propose a general framework of the method as well as several concrete ways of abstracting automata or transducers, which we use for modelling systems and encoding sets of their states as usual in regular model checking. The abstraction is based on collapsing states of automata (or transducers) and its precision is being incrementally adjusted by analysing spurious counterexamples. We illustrate the technique on verification of a wide range of systems including a novel application of automata-based techniques to an example of systems with dynamic linked data structure

Flat counter automata almost everywhere!

This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be ``replaced\u27\u27, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semi-algorithmic technique implemented in successful tools like FAST, LASH or TReX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflict-free Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a emph{uniform} accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass)

Automatic Generation of Invariants for Circular Derivations in {SUP(LA)} 1

The hierarchic combination of linear arithmetic and firstorder logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant problems

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Проверка моделей распределенных систем с помощью аффинного представления данных

A new data structure is suggested for symbolic model checking of distributed systems defined by linear functions of integer variables.Предложено эффективное символьное представление распределенных систем, определяемых линейными функциями над целочисленными переменными

Applying abstract acceleration to (co-)reachability analysis of reactive programs

Acceleration methods are commonly used for computing precisely the effects of loops in the reachability analysis of counter machine models. Applying these methods on synchronous data-flow programs, e.g. Lustre programs, requires to deal with the non-deterministic transformations due to numerical input variables. In this article, we address this problem by extending the concept of abstract acceleration of Gonnord et al. to numerical input variables. Moreover, we describe the dual analysis for co-reachability. We compare our method with some alternative techniques based on abstract interpretation pointing out its advantages and limitations. At last, we give some experimental results