Linear-time Properties Research Articles

Linear-Time Verification of Data-Aware Processes Modulo Theories via Covers and Automata

The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they are intrinsically infinite-state. Existing approaches work for specific datatypes, and/or limit themselves to the verification of safety properties. In this paper, we lift both such limitations, studying for the first time linear-time verification for so-called data-aware processes modulo theories (DMTs), from the foundational and practical point of view. The DMT model is very general, as it supports processes operating over variables that can store arbitrary types of data, ranging over infinite domains and equipped with domain-specific predicates. Specifically, we provide four contributions. First, we devise a semi-decision procedure for linear-time verification of DMTs, which works for a very large class of datatypes obeying to mild model-theoretic assumptions. The procedure relies on a unique combination of automata-theoretic and cover computation techniques to respectively deal with linear-time properties and datatypes. Second, we identify an abstract, semantic property that guarantees the existence of a faithful finite-state abstraction of the original system, and show that our method becomes a decision procedure in this case. Third, we identify concrete, checkable classes of systems that satisfy this property, generalising several results in the literature. Finally, we present an implementation and an experimental evaluation over a benchmark of real-world data-aware business processes.

Model Checking of Possibilistic Linear-Time Properties Based on Generalized Possibilistic Decision Processes

Model checking possibilistic linear-time properties was investigated by Li (2017). However, nondeterminism of the system is absent in previous studies. Therefore, in order to permit both possibilistic and nondeterministic choices, we use the generalized possibilistic decision process (GPDP) as a model of the system. First, the definition of GPDP describing the behavior of nondeterministic system is given in detail, the resolution of nondeterminism is performed by using the notion of schedulers, and the semantics of generalized possibilistic linear-temporal logic (GPoLTL) with schedulers are defined. Second, we study possibilistic model checking of some fuzzy linear-time properties under GPDP. Since there are many (infinite) schedulers satisfying a certain linear timing property in a given state of a GPDP, it is particularly critical to study the optimal strategy and its corresponding possible measure, which is called extremal possibility model checking. For some special fuzzy linear-time properties, such as constrained reachability, step-bounded constrained reachability, reachability, always reachability, repeated reachability, persistence reachability, we present complete solution to the optimal (including maximum and minimum cases) possibilistic model checking of the above reachability using the fixpoint techniques. We also introduce fuzzy !-regular properties in GPDP and show that their model checking can be simplified by repeated reachability. The algorithms for model checking are also provided. Additionally, an example is presented to illustrate the methods described in the paper.

Modeling and Verification of Uncertain Cyber-Physical System Based on Decision Processes

Currently, there is uncertainty in the modeling techniques of cyber-physical systems (CPS) when faced with the multiple possibilities and distributions of complex system behavior. This uncertainty leads to the system’s inability to handle uncertain data correctly, resulting in lower reliability of the system model. Additionally, existing technologies struggle to verify the activity and safety of CPS after modeling, lacking a dynamic verification and analysis approach for uncertain CPS properties.This paper introduces a generalized possibility decision process as a system model. Firstly, the syntax and semantics of generalized possibility temporal logic with decision processes are defined. Uncertain CPS is extended by modeling it based on time-based differential equations and uncertainty hybrid time automaton. After that, model checking is performed on the properties of activity and safety using fuzzy linear time properties. Finally, a cold–hot hybrid constant-temperature system model is used for simulation experiments. By combining theory and experiments, this paper provides a new approach to the verification of uncertain CPS, effectively addressing the state explosion problem. It plays a crucial role in the design of uncertain CPS and offers a key solution for model checking in the presence of uncertainty.

Good-for-Game QPTL: An Alternating Hodges Semantics

An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally express game-theoretic concepts. Inspired by the work on logics of dependence and independence, we provide a new compositional semantics for QPTL that allows for expressing such functional dependencies among variables. The fragment where only restricted quantifications are considered, called behavioral quantifications , allows for linear-time properties that are satisfiable if and only if they are realisable in the Pnueli-Rosner sense. This fragment can be decided, for both model checking and satisfiability , in 2 Exp Time and is expressively equivalent to QPTL , though significantly less succinct.

Measurement Method of Civil Engineering Complexity Structure Based on Logical Equivalent Model

Civil engineering structures are generally large in volume and scale, especially the most commonly used reinforced concrete structures. There are many defects such as micro-cracks and air bubbles inside, and the concrete is easy to crack under tension. The short-gauge length (point) sensor will be affected by local damage and cannot accurately reflect the overall working state of the structure. The long-gauge strain sensing technology can reflect the average strain of the area to be measured when there are local cracks in the structure to be measured and can also be fully deployed on the structure to form a distributed sensor network to comprehensively monitor the entire structure. Therefore, long-gauge length sensing is more suitable for civil engineering structure monitoring. This study mainly focuses on fuzzy systems and introduces a generalized probability decision process model to describe the behavior of such fuzzy systems. The maximum-likelihood scheduling and the minimum-likelihood scheduling are discussed. The corresponding model checking methods for probabilistic linear time properties are final reachability, always reachability, persistent reachability, and repeated reachability, and the advantage of this method is that the verification process of their model checking is transformed into a fuzzy matrix. The model checking problems of generalized likelihood-regular security properties and generalized likelihood-correcting-regular properties are studied, respectively, and their model checking problems are transformed into generalized likelihood linear time properties that are always possible. The failure state of the beam and the displacement of the beam bottom are obtained through the data of each unit sensor. The experimental results show that the sensor can effectively capture the cracks. The measured data of the sensor are relatively accurate. The dynamic test performance of the sensor is studied by the damage monitoring test of the vertical cantilever flat beam. After spectrum analysis, the sensor can accurately obtain the participation coefficient of each mode shape, the recognition result is close to that of the FBG sensor, the frequency recognition error does not exceed 0.2%, and the long-gauge length strain mode of the structure can also be accurately recognized. At the same time, the long-gauge strain mode obtained by the sensor monitoring can accurately locate the damage and can quantitatively identify the damage more accurately.

Simulation Relations for Abstraction-based Robust Control of Hybrid Dynamical Systems

The paper addresses the problem of robust control of hybrid dynamical systems with respect to linear-time properties. First, three notions of robust controllers are formulated, that capture imperfect measurements, actuation errors and delays, and uncertain dynamics, respectively. Under mild assumptions of uniform continuity on the transition relation, robust controller synthesis problem with respect to uncertain dynamics is shown to be more general than those with respect to measurement errors, actuation errors and delays. Hence, the paper focuses on the latter notion of robust controllers. Next, foundations for abstraction-based robust controller synthesis are explored, and uniformly continuous alternating simulation relations are shown to preserve the existence of robust controllers with respect to uncertain dynamics.

From hidden to visible: A unified framework for transforming behavioral theories into rewrite theories

Algebraic formalization and verification are effective and practical ways of modeling and verifying software systems by both model checking and theorem proving techniques. In algebraic approaches, a system can be modeled either in a hidden way as a behavioral theory or in a visible way as a rewrite theory. Several approaches have been proposed to transform behavioral theories into rewrite theories for integrating model checking and theorem proving in verification. In this paper, we propose a framework for transforming behavioral theories into rewrite theories, which unifies four existing related transformation approaches. In this framework, each existing transformation approach can be viewed as a process of transforming behavioral theories first into a special class of behavioral theories and finally into rewrite theories. From this perspective, these transformation approaches differ from each other only in the transformation from ordinary behavioral theories into the classified ones, and their transformations from the classified ones into rewrite theories are essentially the same. We prove that the transformation framework preserves linear-time properties. The preservation of linear-time properties guarantees that a counterexample found by model checking a linear-time property with a generated rewrite theory is also a counterexample in the original behavioral theory, as required by integrated verification.

Quantitative model checking of linear-time properties based on generalized possibility measures

Model checking of linear-time properties based on possibility measures was studied in previous work (Li and Li (2013)). However, the linear-time properties considered in the previous work was qualitative and was based on Boolean logic, the linear-time properties containing possibility information (we call it fuzzy linear-time properties here, which is based on fuzzy logic) of system could not be represented and tackled using the previous methods. We shall study quantitative model checking of fuzzy linear-time properties based on generalized possibility measures in the paper. Both the model of the system, as well as the properties the system needs to adhere to, are described using possibility information to identify the uncertainty in the model/properties. The systems are modeled by generalized possibilistic Kripke structures (GPKS, in short), and the properties are described by fuzzy linear-time properties. Concretely, fuzzy linear-time properties about reachability, always reachability, constrain reachability, repeated reachability and persistence in GPKSs are introduced and studied. Fuzzy regular safety properties and fuzzy ω-regular properties in GPKSs are introduced, the verification of fuzzy regular safety properties and fuzzy ω-regular properties using fuzzy finite automata are thoroughly studied. It has been shown that the verification of fuzzy regular safety properties and fuzzy ω-regular properties in a finite GPKS can be transformed into the verification of (always) reachability properties and repeated reachability (persistence) properties in the product GPKS introduced in this paper. Several examples are given to illustrate the methods presented in the paper.

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.

Quantitative verification and strategy synthesis for stochastic games

Design and control of computer systems that operate in uncertain, competitive or adversarial, environments can be facilitated by formal modelling and analysis. In this paper, we focus on analysis of complex computer systems modelled as turn-based 212-player games, or stochastic games for short, that are able to express both stochastic and non-stochastic uncertainties. We offer a systematic overview of the body of knowledge and algorithmic techniques for verification and strategy synthesis for stochastic games with respect to a broad class of quantitative properties expressible in temporal logic. These include probabilistic linear-time properties, expected total, discounted and average reward properties, and their branching-time extensions and multi-objective combinations. To demonstrate applicability of the framework as well as its practical implementation in a tool called PRISM-games, we describe several case studies that rely on analysis of stochastic games, from areas such as robotics, and networked and distributed systems.

Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties

In this paper, we study a model of quantum Markov chains that is a quantum analogue of Markov chains and is obtained by replacing probabilities in transition matrices with quantum operations. We show that this model is very suited to describe hybrid systems that consist of a quantum component and a classical one. Indeed, hybrid systems are often encountered in quantum information processing. Thus, we further propose a model called hybrid quantum automata (HQA) that can be used to describe the hybrid systems receiving inputs (actions) from the outer world. We show the language equivalence problem of HQA is decidable in polynomial time. Furthermore, we apply this result to the trace equivalence problem of quantum Markov chains, and thus it is also decidable in polynomial time. Finally, we discuss model checking linear-time properties of quantum Markov chains, and show the quantitative analysis of regular safety properties can be addressed successfully.

Model-Checking Linear-Time Properties of Quantum Systems

We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain (closed) subspaces of state Hilbert spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then, an automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and ω--properties recognizable by reversible Büchi automata.

Computation tree logic model checking based on possibility measures

In order to deal with the systematic verification with uncertain information in possibility theory, Li and Li (2013) introduced model checking of linear-time properties in which the uncertainty is modeled by possibility measures. Xue, Lei and Li (2011) defined computation tree logic (CTL) based on possibility measures, which is called possibilistic CTL (PoCTL). This paper is a continuation of the above work. First, we study the expressiveness of PoCTL. Unlike probabilistic CTL, it is shown that PoCTL (in particular, qualitative PoCTL) is more powerful than CTL with respect to their expressiveness. The equivalent expressions of basic CTL formulae using qualitative PoCTL formulae are presented in detail. Some PoCTL formulae that cannot be expressed by any CTL formulae are presented. In particular, some qualitative properties of repeated reachability and persistence are expressed using PoCTL formulae. Next, adapting CTL model-checking algorithm, a method to solve the PoCTL model-checking problem and its time complexity are discussed in detail. Finally, an example is given to illustrate the PoCTL model-checking method.

Model Checking of Linear-Time Properties Based on Possibility Measure

Using possibility measure, we study model checking of linear-time properties in possibilistic Kripke structures. First, the notion of possibilistic Kripke structures and the related possibility measure are introduced, and then, model checking of reachability and repeated reachability linear-time properties in finite possibilistic Kripke structures are studied. Standard safety properties and ω-regular properties in possibilistic Kripke structures are introduced; the verification of regular safety properties and ω-regular properties using finite automata are thoroughly studied. It has been shown that the verification of regular safety properties and ω-regular properties in a finite possibilistic Kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic Kripke structure that is introduced in this paper. Several examples are given to illustrate the methods that are presented in this paper.

Two Variable vs. Linear Temporal Logic in Model Checking and Games

Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear temporal logic (LTL) and two-variable first-order logic (FO2). LTL is more expressive but FO2 can be more succinct, and hence it is not clear which should be easier to verify. We take a comprehensive look at the issue, giving a comparison of verification problems for FO2, LTL, and various sublogics thereof across a wide range of models. In particular, we look at unary temporal logic (UTL), a subset of LTL that is expressively equivalent to FO2; we also consider the stutter-free fragment of FO2, obtained by omitting the successor relation, and the expressively equivalent fragment of UTL, obtained by omitting the next and previous connectives. We give three logic-to-automata translations which can be used to give upper bounds for FO2 and UTL and various sublogics. We apply these to get new bounds for both non-deterministic systems (hierarchical and recursive state machines, games) and for probabilistic systems (Markov chains, recursive Markov chains, and Markov decision processes). We couple these with matching lower-bound arguments. Next, we look at combining FO2 verification techniques with those for LTL. We present here a language that subsumes both FO2 and LTL, and inherits the model checking properties of both languages. Our results give both a unified approach to understanding the behaviour of FO2 and LTL, along with a nearly comprehensive picture of the complexity of verification for these logics and their sublogics.

Layered reasoning for randomized distributed algorithms

Abstract This paper adopts the communication closed layer (CCL) concept of Elrad and Francez to the formal reasoning of randomized distributed algorithms. We do so by enriching probabilistic automata (PA) with a layered composition operator, an intermediate between parallel and sequential composition. Layered composition is used to establish probabilistic counterparts of the CCL laws that exploit independence and/or precedence conditions between the constituent PA. The probabilistic CCL laws enable partial order (po-) equivalence when layered composition is replaced by sequential composition. Such po-equivalence induces a purely syntactic partial-order state space reduction via layered separation in compositions of PA while preserving probabilistic next-free linear-time properties. The feasibility of such layered separation is demonstrated on a randomized mutual exclusion algorithm by Kushilevitz and Rabin, complementing an algebraic approach (for analyzing this algorithm) by McIver, Gonzalia, Cohen, and Morgan.

Linear Time Properties in TLA

Linear Time Properties in TLA

LTL generalized model checking revisited

Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, generalized model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit generalized model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The standard definition of GMC depends on a definition of concretization which is tailored for branching-time model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this weaker preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the model. Finally, we identify classes of formulas for which the model complexity of standard GMC is reduced.

Multi-Objective Model Checking of Markov Decision Processes

We study and provide efficient algorithms for multi-objective model checking problems for Markov Decision Processes (MDPs). Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi\_i, and probabilities r\_i \epsilon [0,1], i=1,...,k, we ask whether there exists a strategy \sigma for the controller such that, for all i, the probability that a trajectory of M controlled by \sigma satisfies \varphi\_i is at least r\_i. We provide an algorithm that decides whether there exists such a strategy and if so produces it, and which runs in time polynomial in the size of the MDP. Such a strategy may require the use of both randomization and memory. We also consider more general multi-objective \omega -regular queries, which we motivate with an application to assume-guarantee compositional reasoning for probabilistic systems. Note that there can be trade-offs between different properties: satisfying property \varphi\_1 with high probability may necessitate satisfying \varphi\_2 with low probability. Viewing this as a multi-objective optimization problem, we want information about the "trade-off curve" or Pareto curve for maximizing the probabilities of different properties. We show that one can compute an approximate Pareto curve with respect to a set of \omega -regular properties in time polynomial in the size of the MDP. Our quantitative upper bounds use LP methods. We also study qualitative multi-objective model checking problems, and we show that these can be analysed by purely graph-theoretic methods, even though the strategies may still require both randomization and memory.

Parallel Model Checking Large-Scale Genetic Regulatory Networks with DiVinE

Studies of cells in silico can greatly reduce the need for expensive and prolonged laboratory experimentation. The use of model checking for the analysis of biological networks has attracted much attention recently. One of the practical limitations is the size of the model. In the paper we report on parallel model checking of genetic regulatory network using the model-checker DiVinE. The approach can check linear time properties on large networks.