A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published in the the Proceedings of TACAS 2007, LNCS 442

Parameterized Model-Checking for Timed-Systems with Conjunctive Guards (Extended Version)

In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an \emph{apriori} unknown number of Timed Automata instantiated from a finite set $U_1, \dots, U_n$ of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

Reasoning about Actions with Temporal Answer Sets

In this paper we combine Answer Set Programming (ASP) with Dynamic Linear Time Temporal Logic (DLTL) to define a temporal logic programming language for reasoning about complex actions and infinite computations. DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. The action language allows general DLTL formulas to be included in domain descriptions to constrain the space of possible extensions. We introduce a notion of Temporal Answer Set for domain descriptions, based on the usual notion of Answer Set. Also, we provide a translation of domain descriptions into standard ASP and we use Bounded Model Checking techniques for the verification of DLTL constraints.Comment: To appear in Theory and Practice of Logic Programmin

Tracing monadic computations and representing effects

In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a computation. To make that possible, in this paper we introduce monad transformers that add the ability to automatically accumulate observations about the course of execution as an effect. We discover that if we treat the resulting trace as the actual result of the computation, we can find new functionality in existing monads, notably when working with non-terminating computations.Comment: In Proceedings MSFP 2012, arXiv:1202.240