Counting LTL

The original publication is available at ieeexplore.ieee.org.International audienceThis paper presents a quantitative extension for the linear-time temporal logic LTL allowing to specify the number of states satisfying certain sub-formulas along paths. We give decision procedures for the satisfiability and model checking of this new temporal logic and study the complexity of the corresponding problems. Furthermore we show that the problems become undecidable when more expressive constraints are considered

Flat Model Checking for Counting LTL Using Quantifier-Free Presburger Arithmetic

This paper presents an approximation approach to verifying counter systems with respect to properties formulated in an expressive counting extension of linear temporal logic. It can express, e.g., that the number of acknowledgements never exceeds the number of requests to a service, by counting specific positions along a run and imposing arithmetic constraints. The addressed problem is undecidable and therefore solved on flat under-approximations of a system. This provides a flexibly adjustable trade-off between exhaustiveness and computational effort, similar to bounded model checking. Recent techniques and results for model-checking frequency properties over flat Kripke structures are lifted and employed to construct a parametrised encoding of the (approximated) problem in quantifier-free Presburger arithmetic. A prototype implementation based on the z3 SMT solver demonstrates the effectiveness of the approach based on problems from the RERS Challange

On Relaxing Metric Information in Linear Temporal Logic

Metric LTL formulas rely on the next operator to encode time distances, whereas qualitative LTL formulas use only the until operator. This paper shows how to transform any metric LTL formula M into a qualitative formula Q, such that Q is satisfiable if and only if M is satisfiable over words with variability bounded with respect to the largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances. Besides the theoretical interest, this result can help simplify the verification of systems with time-granularity heterogeneity, where large distances are required to express the coarse-grain dynamics in terms of fine-grain time units.Comment: Minor change

Computing Bounds for Counter Automata

Qualitative formal verification, that seeks Boolean answers about the behavior of a system, is often insufficient for practical purposes. Observing quantitative information is of greater interest, e.g. for the calibration of a battery or a real-time scheduler. Historically, the focus has been on quantities in continuous domain, but recent years showed a renewed interest for discrete quantitative domains. Counter Automata (CA) is a quantitative extension of classical omega-automata. Recently a nice theory has been developed for them that extends the qualitative setting, with counterparts in terms of logics, automata and algebraic structure. We propose an adaptation, with plenty of practical applications,  of this formalism to express properties over discrete quantitative domains. The behavior of a Counter Automaton defines a function from infinite words to integers. Finding the bounds of such a function over a given set of words can be seen as an extension of qualitative universal and existential model-checking. Although the problem of determining whether such bounds are finite have already been addressed, efficient algorithms to compute their exact values still lack. We propose an non-naive method for the computation of the exact values of these bounds. It relies on a generalization of the emptiness problem of omega-automata. To solve this generalized emptiness problem, we propose an algorithm that extends emptiness check algorithms based on SCC enumeration.