Linear-time Temporal Logic Specifications Research Articles

Liveness in broadcast networks

We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is Liveness Verification. It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be texttt {P}-hard but in texttt {EXPSPACE}. We close the gap by a polynomial-time algorithm. The latter relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is Fair Liveness Verification. It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is Fair Model Checking. It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to Liveness Verification. The second problem is Sparse Model Checking. It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to Fair Liveness Verification.

Specifying a Timestamp-based Protocol For Multi-step Transactions Using LTL

Most of the concurrent transactional protocols consider serializability as a correctness criterion of the transactions execution. Usually, the proof of the serializability relies on mathematical proofs for a fixed finite number of transactions. In this paper, we introduce a protocol to deal with an infinite number of transactions which are iterated infinitely often. We specify serializability of the transactions and the protocol using a specification language based on temporal logics. It is worthwhile using temporal logics such as LTL (Lineartime Temporal Logic) to specify transactions, to gain full automatic verification by using model checkers. Keywords—Multi-step transactions, LTL specifications, Model Checking.

Diagnosis of repeated failures for discrete event systems with linear-time temporal-logic specifications

In our earlier work, we introduced a state-based approach for the diagnosis of repeatedly occurring failures in discrete event systems (DESs). Since temporal logic provides a simpler way of specifying system properties; in this paper, a temporal-logic-based approach for diagnosing the occurrence of a repeated number of failures is developed. Linear-time temporal-logic (LTL) formulae are used to represent the specifications of DESs. Notions of prediagnosability for failures and diagnosability for repeated failures are introduced in the setting of temporal logic. A polynomial algorithm for the test of prediagnosability for failures is provided. The diagnosis problem for repeated failures in the temporal-logic setting is reduced to one in a state-based setting, and so the prior results of a state-based repeated failure diagnosis can be applied. Finally, a simple example is given for illustration. Note to Practitioners-Certain failures in a system are repeatable, such as routing errors in a manufacturing system. A theory for the diagnosis of such failures was presented in an earlier work of Jiang et al. The present paper uses temporal logic to specify such failures. It turns out that repeatable failures can be specified as violations of invariant properties (i.e., properties that must always hold). Given an invariant property that the system must always satisfy, an algorithm is presented to refine the system model and label those states of the refined system where the property is violated. The problem of repeated diagnosis then requires determining, within a bounded delay, each time a "failure-state" is visited. For this analysis, the existing theory developed by Jiang et al. is used.

Failure Diagnosis of Discrete-Event Systems With Linear-Time Temporal Logic Specifications

The paper studies failure diagnosis of discrete-event systems (DESs) with linear-time temporal logic (LTL) specifications. The LTL formulas are used for specifying failures in the system. The LTL-based specifications make the specification specifying process easier and more user-friendly than the formal language/automata-based specifications; and they can capture the failures representing the violation of both liveness and safety properties, whereas the prior formal language/automaton-based specifications can capture the failures representing the violation of only the safety properties (such as the occurrence of a faulty event or the arrival at a failed state). Prediagnosability and diagnosability of DESs in the temporal logic setting are defined. The problem of testing prediagnosability and diagnosability is reduced to the problem of model checking. An algorithm for the test of prediagnosability and diagnosability, and the synthesis of a diagnoser is obtained. The complexity of the algorithm is exponential in the length of each specification LTL formula, and polynomial in the number of system states and the number of specifications. The requirement of nonexistence of unobservable cycles in the system, which is needed for the diagnosis algorithms in prior methods to work, is relaxed. Finally, a simple example is given for illustration.

An improvement of partial-order verification

Partial-order reduction methods form a collection of state exploration techniques set to relieve the state-explosion problem in concurrent program verification. Their use often reduces significantly the memory needed for verifying local and termination properties of concurrent programs and, moreover, for verifying that concurrent programs satisfy their linear-time temporal logic specifications (i.e. for LTL model-checking). One particular such method is implemented in the verification system SPIN, which is considered to be one of the most efficient and most widely used LTL model-checkers. This paper builds on SPIN's partial-order reduction method to yield an approach that enables further space reductions for verifying concurrent programs. © 1998 John Wiley & Sons, Ltd.

Assumption/guarantee specifications in linear-time temporal logic

An assumption/guarantee specification of a system consists of an assumption part, which specifies the assumptions on the behavior of the environment, and a guarantee part, which specifies the properties guaranteed by the system if the environment obeys the assumptions. A suitable interpretation of an assumption/guarantee specification was essentially formulated by Misra and Chandy (1981). The interpretation was later extended by others to allow liveness properties in the guarantee part. In this paper, we explore the use of linear-time temporal logic in writing and reasoning about assumption/guarantee specifications. We choose this logic, specifically LTL defined in the book by Manna and Pnueli (1992), for the following reasons: (i) Linear-time temporal logics, including LTL and TLA, have proven to be a successful formalism for the specification and verification of concurrent systems. (ii) Previous works on assumption/guarantee specifications typically reason about relevant properties at the semantic level or define a special-purpose logic. We feel it is beneficial to formulate such specifications in a more widely used formalism. (iii) We find that, with past temporal operators, LTL admits a succinct syntactic formulation of assumption/guarantee specifications. This contrasts, in particular, with the work by Abadi and Lamport using TLA, where working at the syntactic level is more complicated. We derive inference rules for refining and composing assumption/guarantee specifications as the main results of this paper. The derived rules can handle internal variables. We had to overcome a number of technical problems in this pursuit, in particular, the problem of extracting the safety closure of a temporal formula. As a by-product, we identify general conditions under which the safety closure can be expressed in a succinct way that facilitates syntactic manipulation.

A stubborn attack on state explosion

The paper presents the LTL preserving stubborn set method for reducing the amount of work needed in the automatic verification of concurrent systems with respect to linear time temporal logic specifications. The method facilitates the generation of reduced state spaces such that the truth values of a collection of linear temporal logic formulas are the same in the ordinary and reduced state spaces. The only restrictions posed by the method are that the collection of formulas must be known before the reduced state space generation is commenced, the use of the temporal operator “next” is prohibited, and the (reduced) state space of the system must be finite. The method cuts down the number of states by utilising the fact that in concurrent systems the nett result of the occurrence of two events is often independent of the order of occurrence.