Multi-valued Model Checking Research Articles

Multi-valued verification of commitment systems with uncertainty and inconsistency in multi-source data settings

In the dynamic landscape of Internet of Things (IoT) applications within multi-source data environments, ensuring the reliability and correctness of system communications has become a paramount concern. This is particularly evident in the presence of commitment protocols with inconsistency and uncertainty. This paper tackles these challenges by introducing a new logic, termed Six-Values Computation Tree Logic for Commitment (6V-CTLC), specifically crafted to adeptly model IoT systems with both inconsistency and uncertainty. Employing this logic, we devise an innovative reduction-based multi-valued model checking approach to verify the systems under scrutiny. Our method is implemented through a Java transformation tool we developed to translate the 6V-CTLC logic to the classical logic of commitment (CTLC) and seamlessly interfaces with the efficient model checker MCMAS+. Applying this approach, we verify an abstracted 6V-CTLC model featuring uncertainty and inconsistency, as well as the original model of our system before abstraction. Furthermore, we assess the scalability of our approach through ten experiments, comparing the results obtained from verifying the two models. The findings demonstrate the effectiveness of system abstraction in mitigating the state explosion problem, while the developed multi-valued model checking technique yields precise results.

Verifying trust over IoT-ad hoc network-based applications under uncertainty

The rapid integration of the Internet of Things (IoT) with ad hoc networks offers significant advantages for revolutionizing smart environments. However, ensuring trust and reliability within these interconnected systems remains a significant challenge. To address this challenge, this paper introduces an innovative three-valued (3v) trust model customized specifically for IoT-ad hoc systems. The model employs three-valued logic to evaluate trust in social commitments within ambiguous scenarios, where commitments serve as the foundation of the business logic. Our aim is to enhance the effectiveness and economic feasibility of IoT in smart environments. To advance this initiative, we introduce the 3v-TCTLC, a distinctive modeling language that extends the conventional two-valued logic by introducing a third value to accommodate uncertainty. This novel approach facilitates the assessment of trust in commitments within uncertain IoT-ad hoc environments. Additionally, we improve the functionality of the “MACMAS-interactor” tool, incorporating new features to support our 3v-TCTLC logic. Through two case studies in the domains of smart health monitoring and smart home systems, we validate our model against specific requirements in uncertain contexts. These case studies highlight the robustness and practicality of our proposed tools and methodologies. Compared to prevalent trust management strategies employed in IoT and ad-hoc networks, our methodology stands out distinctly. While many current solutions propose trust-centered protocols, with some even harnessing advanced technologies, they frequently overlook the crucial element of model checking. Our approach not only incorporates this critical component but also ensures the integrity of the system. Furthermore, even though the field of multi-valued model checking has seen advancements like χCTL, our research contributes significantly by integrating trust and commitment verification specifically designed for IoT-ad hoc environments. Our empirical assessments in the domains of smart health and home systems confirm that our tool and strategies demonstrate superior performance in terms of time and space usage and better adaptability and scalability in uncertain scenarios, representing a noteworthy advancement over existing techniques and tools.

Computation tree logic model checking based on multi-valued possibility measures

Multi-valued model checking has been studied extensively recently, but important uncertain information contained in systems of multi-valued logics has not been considered in previous work and, as a consequence, some serious deficiencies arise. To make up for these deficiencies, this paper considers the possibility information implied in multi-valued systems. Precisely, we investigate computation tree logic model checking based on multi-valued possibility measures. We model multi-valued logic systems by multi-valued Kripke structures (MvKSs) and specify their verification properties by multi-valued computation tree logic (MvCTL) formulae. Based on generalized possibility measures and generalized necessity measures, an MvCTL model checking method is proposed, the pseudocode of the corresponding model checking algorithm is presented, and its time complexity is analyzed in detail. Furthermore, after detailed comparisons with χCTL (introduced in Chechik et al. [10]) and the classical CTL, we show that MvCTL is more general than χCTL, but cannot be reduced to the classical CTL. The conditions on lattice and MvKS under which MvCTL is equivalent to χCTL are given. Finally, some examples and a case study are given to illustrate the MvCTL model-checking method.

Model checking software product lines based on feature slicing

Feature model is a popular formalism for describing the commonality and variability of a software product line in terms of features. Feature models symbolise a presentation of the possible application configuration space, and can be customised based on specific domain requirements and stakeholder goals. As feature models are becoming increasingly complex, it is desired to provide automatic support for customised analysis and verification based on the specific goals and requirements of stakeholders. This paper first presents feature model slicing based on the requirements of the users. We then introduce three-valued abstraction of behaviour models based on the slicing unit. Finally, based on multi-valued model checker, a case study was conducted to illustrate the effectiveness of our approach.

Model checking of linear-time properties in multi-valued systems

In this paper, we study the model-checking problem of linear-time properties in multi-valued systems. Safety properties, invariant properties, liveness properties, persistence and dual-persistence properties in multi-valued logic systems are introduced. Some algorithms related to the above multi-valued linear-time properties are discussed. The verification of multi-valued regular safety properties and multi-valued ω-regular properties using lattice-valued automata are thoroughly studied. Since the law of non-contradiction (i.e., a∧¬a=0) and the law of excluded-middle (i.e., a∨¬a=1) do not hold in multi-valued logic, the linear-time properties introduced in this paper have new forms compared to those in classical logic. Compared to those classical model-checking methods, our methods to multi-valued model checking are accordingly more direct: We give an algorithm for showing TS⊧P for a model TS and a linear-time property P, which proceeds by directly checking the inclusion Traces(TS) ⊆ P instead of Traces(TS)∩¬P=∅. A new form of multi-valued model checking with membership degree is also introduced. In particular, we show that multi-valued model checking can be reduced to classical model checking. The related verification algorithms are also presented. Some illustrative examples and a case study are also provided.

Model checking computation tree logic over finite lattices

Multi-valued model-checking is an extension of classical model-checking used to verify the properties of systems with uncertain information content. It is used in systems where the semantic domain of both the models of the systems and the specification is a De Morgan algebra or more abstract structure such as semirings. A common feature of De Morgan algebras and semirings is that they satisfy the distributive law, which is crucial for all of the multi-valued model-checking algorithms developed so far. In this paper, we study computation tree logic with membership values in a finite lattice, which are called multi-valued computation tree logic (MCTL). We introduce three semantics for MCTL over the multi-valued Kripke structure: path semantics, fixpoint semantics, and algebraic semantics, and prove that they coincide if and only if the underlying lattice is distributive. Furthermore, we provide model-checking algorithms with respect to the three semantics. Our algorithms show that MCTL model-checking problems with respect to the fixpoint and algebraic semantics can be solved in polynomial time in the size of the state space of the multi-valued Kripke structure, the size of the lattice, and the length of the formula, while MCTL model-checking problem with respect to the path semantics is in PSPACE. We also provide a lower bound for the MCTL model-checking problem with respect to the path semantics.

Data structures for symbolic multi-valued model-checking

Multi-valued logics provide an interesting alternative to classical boolean logic for modeling and reasoning about systems. Such logics can be used for reasoning about partially-specified systems, effectively encode vacuity detection and query-checking problems, help in detecting inconsistencies, and many others.In our earlier work, we identified a useful family of multi-valued logics: those specified over finite distributive lattices where negation preserves involution, i.e., \({{\neg}}{{\neg}} a = a\) for every element a of the logic. Such structures are called quasi-boolean algebras, and model-checking over these not only extends the domain of applicability of automated reasoning to new problems, but can also speed up solutions to some classical verification problems.Symbolic model-checking over quasi-boolean algebras can be cast in terms of operations over multi-valued sets: sets whose membership functions are multi-valued. In this paper, we propose and empirically evaluate several choices for implementing multi-valued sets with decision diagrams. In particular, we describe two major approaches: (1) representing the multi-valued membership function canonically, using MDDs or ADDs; (2) representing multi-valued sets as a collection of classical sets, using a vector of either MBTDDs or BDDs. The naive implementation of (2) includes having a classical set for each value of the algebra. We exploit a result of lattice theory to reduce the number of such sets that need to be represented.The major contribution of this paper is the evaluation of the different implementations of multi-valued sets, done via a series of experiments and using several case studies.

Multi-valued symbolic model-checking

This article introduces the concept of multi-valued model-checking and describes a multi-valued symbolic model-checker, ΧChek. Multi-valued model-checking is a generalization of classical model-checking, useful for analyzing models that contain uncertainty (lack of essential information) or inconsistency (contradictory information, often occurring when information is gathered from multiple sources). Multi-valued logics support the explicit modeling of uncertainty and disagreement by providing additional truth values in the logic.This article provides a theoretical basis for multi-valued model-checking and discusses some of its applications. A companion article [Chechik et al. 2002b] describes implementation issues in detail. The model-checker works for any member of a large class of multi-valued logics. Our modeling language is based on a generalization of Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multi-valued logic. Properties are expressed in ΧCTL, our multi-valued extension of the temporal logic CTL.We define the class of logics, present the theory of multi-valued sets and multi-valued relations used in our model-checking algorithm, and define the multi-valued extensions of CTL and Kripke structures. We explore the relationship between ΧCTL and CTL, and provide a symbolic model-checking algorithm for ΧCTL. We also address the use of fairness in multi-valued model-checking. Finally, we discuss some applications of the multi-valued model-checking approach.

Temporal logic query checking: a tool for model exploration

Temporal logic query checking was first introduced by W. Chan in order to speed up design understanding by discovering properties not known a priori. A query is a temporal logic formula containing a special symbol ?/sub 1/, known as a placeholder. Given a Kripke structure and a propositional formula /spl phi/, we say that /spl phi/ satisfies the query if replacing the placeholder by /spl phi/ results in a temporal logic formula satisfied by the Kripke structure. A solution to a temporal logic query on a Kripke structure is the set of all propositional formulas that satisfy the query. Query checking helps discover temporal properties of a system and, as such, is a useful tool for model exploration. In this paper, we show that query checking is applicable to a variety of model exploration tasks, ranging from invariant computation to test case generation. We illustrate these using a Cruise Control System. Additionally, we show that query checking is an instance of a multi-valued model checking of Chechik et al. This approach enables us to build an implementation of a temporal logic query checker, TLQSolver, on top of our existing multi-valued model checker /sub /spl chi//Chek. It also allows us to decide a large class of queries and introduce witnesses for temporal logic queries-an essential notion for effective model exploration.