Verifying nondeterministic probabilistic channel systems against ω\omega-regular linear-time properties

Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been introduced, where it can be decided whether a linear-time property holds almost surely. However, such fully probabilistic systems are not a faithful model of nondeterministic protocols. We study a hybrid model for LCSs where losses of messages are seen as faults occurring with some given probability, and where the internal behavior of the system remains nondeterministic. Thus the semantics is in terms of infinite-state Markov decision processes. The purpose of this article is to discuss the decidability of linear-time properties formalized by formulas of linear temporal logic (LTL). Our focus is on the qualitative setting where one asks, e.g., whether a LTL-formula holds almost surely or with zero probability (in case the formula describes the bad behaviors). Surprisingly, it turns out that -- in contrast to finite-state Markov decision processes -- the satisfaction relation for LTL formulas depends on the chosen type of schedulers that resolve the nondeterminism. While all variants of the qualitative LTL model checking problem for the full class of history-dependent schedulers are undecidable, the same questions for finite-memory scheduler can be solved algorithmically. However, the restriction to reachability properties and special kinds of recurrent reachability properties yields decidable verification problems for the full class of schedulers, which -- for this restricted class of properties -- are as powerful as finite-memory schedulers, or even a subclass of them.Comment: 39 page

Encoding Synchronous Interactions Using Labelled Petri Nets

International audienceWe present an encoding of (bound) CSP processes with replication into Petri nets with labelled transitions. Through the encoding, the firing semantics of Petri nets models the standard operational semantics of CSP processes, which is both preserved and reflected. This correspondence allows for describing by net semantics the standard CSP observational equivalences. Since the encoding is modular with respect to process syntax, the paper puts on a firm ground the technology transfer between the two formalisms, e.g. recasting into the CSP framework well-established results like decidability of coverability for nets. This work complements previous results concerning the encoding of asynchronous interactions, thus witnessing the expressiveness of (open) labelled nets in modelling process calculi with alternative communication patterns

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

Analysis of the reachability problem in fragments of the Pi-calculus

BSc Thesis from Universidad del Valle, ColombiaThe pi-calculus is one of the most important formalisms for analyzing and modelling concurrent systems. It is a simple but powerful tool for specifying and checking several properties in this kind of systems. An interesting property of any system is the ability to reach some special state where it has a particular behavior. In security systems this is extremely important, since we would like that a system does not reach a state where a secret becomes observable to potential attackers. This work studies the reachability problem in fragments of the pi-calculus and explores some expressiveness results beyond this problem. We prove the relation between local names and sequences of actions in CCS! processes. Using this result and the decidability of barbs from previous work we prove that the reachability problem for some fragments of pi-calculus is decidable. We also provide an algorithmic approach for solving this problem using the theory of well-structured transition systems in consequence we are able to verify this property in infinite state systems with a finite number of steps. Finally, we provide a small interpreter for CCS!, useful as an initial practical approach for checking properties in real life systems specified by this calculu

Analysis of the reachability problem in fragments of the Pi-calculus

BSc Thesis from Universidad del Valle, ColombiaThe pi-calculus is one of the most important formalisms for analyzing and modelling concurrent systems. It is a simple but powerful tool for specifying and checking several properties in this kind of systems. An interesting property of any system is the ability to reach some special state where it has a particular behavior. In security systems this is extremely important, since we would like that a system does not reach a state where a secret becomes observable to potential attackers. This work studies the reachability problem in fragments of the pi-calculus and explores some expressiveness results beyond this problem. We prove the relation between local names and sequences of actions in CCS! processes. Using this result and the decidability of barbs from previous work we prove that the reachability problem for some fragments of pi-calculus is decidable. We also provide an algorithmic approach for solving this problem using the theory of well-structured transition systems in consequence we are able to verify this property in infinite state systems with a finite number of steps. Finally, we provide a small interpreter for CCS!, useful as an initial practical approach for checking properties in real life systems specified by this calculu

General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and Beyond

The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous programs that capture all known results as well as show decidability of new and important classes. As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs -- such as OCaml programs using Lwt -- and undecidability of liveness verification already for order-2 asynchronous programs. We show that under mild assumptions, surprisingly, safety and termination verification of asynchronous programs with handlers from a language class are decidable iff emptiness is decidable for the underlying language class. Moreover, we show that configuration reachability and liveness (fair termination) verification are equivalent, and decidability of these problems implies decidability of the well-known "equal-letters" problem on languages. Our results close the decidability frontier for asynchronous programs

Reachability in Concurrent Uninterpreted Programs

We study the safety verification (reachability problem) for concurrent programs with uninterpreted functions/relations. By extending the notion of coherence, recently identified for sequential programs, to concurrent programs, we show that reachability in coherent concurrent programs under various scheduling restrictions is decidable by a reduction to multistack pushdown automata, and establish precise complexity bounds for them. We also prove that the coherence restriction for these various scheduling restrictions is itself a decidable property